The Scot required several hours of treatment following his first-round doubles match with Australian partner John Peers on Thursday.
Murray revealed he did not prepare properly for the match, which was played in temperatures in excess of 40C, because he overslept for an hour and a half.
He said: "My alarm didn't go off so I slept in about an hour and a half later than what I should have. I was only woken up because the driver called the room to see where I was.
"That was 8.30am and we were supposed to practise at 9am, then the match was 11am. I was kind of rushing around, I didn't get time to have breakfast and all that stuff, so it wasn't an ideal start.
"I'm sure I would have been okay if I hadn't had the start to the day that I had. I know the risks you take by going out in that heat and not being fully prepared. I didn't choose to do it that way, it's just what happened."
Describing his ordeal, he said: "I started feeling bad after the match and when I got back into the changing rooms I felt light-headed.
"I just wanted to lie down and then I started to cramp in my legs, which was a bit worrying for me because I'd never had it that bad before.
"The doctors and the physios were putting ice over me, so then I was shivering for a long time. I was on the floor in the locker room. I didn't want to move.
"Finally the physio said I needed to get up and walk around, and after I got up I felt a lot better straight away.
"I still felt rough for a while, I couldn't really sit down. I was walking around the grounds for a couple of hours because every time I sat down I started getting really light-headed. But in the evening I felt a lot better and once I slept I was fine.
"It was a bit scary but I'm here today and you would never know it had happened."
Murray was far from the only player to struggle in the conditions, which were branded "inhumane" by Canada's Frank Dancevic after he blacked out on court.
The extreme heat policy, which sees matches either suspended or played under a roof, was implemented only once despite the thermometer reading 40C on four successive days.
Murray, brother of world number four Andy Murray, was reluctant to comment on the rights or wrongs of the decision-making, saying with a wry smile: "It's above my pay grade really.
"They've obviously got to decide and that day after we finished they thought it was too hot to play. I don't think too many people would have complained if they'd stopped the previous days."
Murray insisted he had recovered fully for his second-round match on Saturday, but he and Peers were beaten 6-4 6-4 by America's Eric Butorac and Raven Klaasen of South Africa.
The British-Australian pair of Murray and Peers had an excellent 2013 and went close to qualifying for the ATP World Tour Finals in London despite only playing together in two Masters Series events.
They are now ranked highly enough to get into all the big events, and being among the top eight teams in the world at the O2 Arena in November is a big goal.
"We were only a couple of matches short at the end so we'll keep working hard, working together and trying to make the team stronger," said Murray.
"Because we can play in the bigger tournaments now, there's more points available, so hopefully that will stand us in good stead. But obviously the players are stronger as well so we'll have to play well to win matches."