He sniffs the air. He gazes rapturously upwards. If he does not quite get down and kiss the blessed Tarmac, be assured that only a bad knee prevents such an act of homage. "Let me just breathe it in," he says. "Ah, alma mater. I remember on my first day here thinking, 'This is the most beautiful building in the world.' What a sight!"
Coltrane, or Robin McMillan as he still was then, studied at the art school between 1968 and 1972 and lived in a bedsit in Cecil Street, a shortish daunder to the west. His Great Great Uncle Sandy had stayed in nearby Garnethill Street and could remember seeing Charles Rennie Mackintosh, walking in the company of his patron, Miss Cranston, black cloaks billowing behind them, as the architect chalked marks on the now famous front doors to show where the windows should be cut. This would have been about 1899, but Coltrane, in his vivid telling of the anecdote, makes it sound as though it was a week last Tuesday.
Still, we are not here to talk about the past, not just yet. First there is the new Reid building to visit. Costing £50 million, it rises to five storeys directly across Renfrew Street from the Mackintosh building. Inside, it is vast, open and white, its most notable feature being the "driven voids" - giant concrete cones that funnel throughout every level as much daylight as the grudging Glasgow sky will allow. Coltrane is especially taken with these - "Oh my God, that's wonderful!" - but he does not have long to ponder this marvel.
Standing at the bottom of the shaft, he is approached by two weaving students, Emily and Kirsty, who ask for a picture. They ask what he studied when he was at art school. Drawing and painting, he tells them. "We were the aristocrats. We used to wear blue flared jeans and clean our fingers on them. So we wandered round looking like a Jackson Pollock, basically, and all the girls said, 'Are you in drawing and painting?' 'Maybe.' And then you'd just flick your long hair and play another Jimi Hendrix track."
Touring the art school with Coltrane must be what it is like visiting somewhere with the Queen, that is if Her Majesty kept breaking off to tell risque anecdotes and nipping out for a fag break. There are smiles, handshakes and photographs wherever he goes. A crane driver working on the building offers to let him drive, an offer Coltrane regally declines. Stopping in the Vic bar for a drink, he sympathises with a young woman on the subject of her boyfriend's Buckfast breath, and contemplates the menu with a sceptical eye - "Halloumi? In my day it was all sausage rolls, chips, Spam, Spam, Spam and Spam."
What was Coltrane like at that time? "I was deeply pretentious," he says. "I was not remotely interested in all this pop culture nonsense and people painting aeroplanes. I thought I could do that on the back of an envelope. Whereas I wanted to paint like the painters who really moved me, who made me want to weep about humanity. Titian. Rembrandt. But I looked at my diploma show and felt a terrible disappointment when I realised all the things that were in my head were not on the canvas. I felt there was something wrong with my hands. That was a heartbreaking day, I have to say. I still regret that because I still have visual ideas all the time, which is why I wanted to direct films." Conscious that he might be sounding a bit woe-is-me, he raises an eyebrow, an eyebrow in which is implied every Bafta he has ever won, every box office dollar earned. "But, hey, have I suffered? I weathered that storm."
Coltrane will be 64 at the end of March and feels his best years as an actor are still ahead of him. He seems younger than his age. He points out his fancy shirt, covered in cartoon vehicles from the movie Cars, a gift from Pixar's John Lasseter, no doubt as a thank you for his voice work on Brave. He is also wearing a dark blue suit, made for him by the tailor Steven Purvis, an art school contemporary, who, in 1972, made Coltrane his first suit - denim with lapels reaching almost beyond the sharp shoulders - of which he still thinks fondly. Liz Lochhead was also at art school with Coltrane. "Liz and I used to read poems to each other," he recalls. "She wrote endlessly. It was quite unusual in those days to be into literature at art school. It was all sex and drugs and rock 'n' roll, and they weren't really interested in words."
We cross Renfrew Street to the Mackintosh building. Coltrane was in his teens when he first walked up these steps and in these doors. He had attended private school at Glenalmond where he swapped his Glasgow accent for Prince Charles-ish plumminess to fit in. When this didn't go down well at the art school, he swapped back. "Most of the students were working class guys, so I got rejected for being a bit posh, but you adapt and you survive; you meet people and you realise that though they were born in Drumchapel and you were born in Rutherglen, you actually share the same values. We were all artistic and wanted to make the world a better place by drawing and painting. There was a real shared passion."
His personal reinvention as weegie bohemian was a sort of scale model of the wider cultural transformation of the time. Feminism, gay lib, the peace movement, the Pill, trade unionism - all these things were swirling through the joint-scented air. Indeed, one attempt by Coltrane to help support the 1971 campaign by workers to keep the Glasgow shipyards open led to him being given "a bollocking" by the director of the art school. "It was nothing serious," he demurs. "We were all being political in those days. I believe I showed a pornographic movie and charged people five shillings to look at it and gave the money to Upper Clyde Shipbuilders."
Spotting a wooden, paint-smeared door with the number 42 written on it in brass numerals, Coltrane is buzzing. "I think this is my old studio! Oh God, I want to go in there right now. Would they let me?" He does not wait to find out, walking straight in, breathing deep the smell of linseed oil and causing quite a stir among students preparing for their end-of-year shows, who are more than a little surprised to find Rubeus Hagrid asking them questions about their work and - on spotting a ceramic sink - reminiscing about how certain tutors used to come back from lunchtime sessions in the Art Club and relieve their beery bladders in front of everyone.
Every inch of the building seems to prompt a different memory, and not all of them from his student days. In the loggia, an arched corridor with incredible views over Glasgow, Coltrane recalls it as a filming location. "This is where we shot Tutti Frutti. It was the scene where Danny admitted he is in love with Suzi." He wanders further along the corridor and into another studio; he wants to show me a room, a sort of greenhouse, where students would sketch botanical specimens. "Forgive me," he says to a bemused young man who had been busy painting. "I'm just trying to work out how you get through to the old bit where they used to keep the plants?"
The student points to a wall. "They've built that in front of it now."
"Bastards!" says Coltrane. "We used to grow dope in there in the sixties."
He began acting while at art school. The liberal studies class was taken by the poet Stephen Mulrine, who would stage plays. Coltrane appeared in Pinter's The Dumb Waiter (Liz Lochhead recalls his performance as "fantastic … bloody terrifying") and a drama teacher in the audience told him that he had talent. This, at a time when he was realising he would never be as good a painter as he had hoped, was hugely encouraging. The head of painting tried to talk him out of an acting career, saying that film was a fad that would never take off, but young long-haired, paint-splattered Robin McMillan felt that his future lay on stage and screen. Robbie Coltrane was waiting in the wings.
"I guess I kind of grew up here is the truth," he says. "It opened my mind up in so many ways. When I came to the art school I was a plump 18-year-old public schoolboy. When I left I was" - and here he adopts the booming tones of a movie trailer voiceover - "a citizen of the world."