However, last night the 43-year-old made the sort of noises that might have warmed even the most abject, stony-hearted Hibby of these days.
Dempster spoke to Hibernian TV and others and laid a number of issues on the line. Terry Butcher's future, she said, was too soon to call - she will be meeting him next week. As for Rod Petrie, the embattled Hibs chairman, Dempster robustly claimed that he would have no interference in the decisions and changes she intends to start making around the club.
Hibs are in the grip of a fans revolt. A mass protest is planned today at Easter Road and there have been incessant demands for Petrie to go, with some also wanting Butcher evicted. The recent relegation from the SPFL Premiership has plunged Dempster and Hibs into a minor nightmare.
"It has not been the best introduction for me, to be honest," said Dempster. "It has been very difficult. You can tell from the noises coming from the broad supporter-base that we are not in a great place. I need to deal with that and resolve it as best as possible.
"But I feel confident, I'm optimistic. I understand football and have a lot of experience. I'm not coming in to this cold. I've got great contacts, great connections. I think I've got qualities that are needed at this club right now."
As Hibs supporters hear more from Dempster, the truth is, they might be slightly startled. Petrie has ruled the club from a kind of icy distance, almost with a North Korean detachment: a mysterious leader whom few got to know. Yet here is Dempster, open and willing with the media and anyone else, despite all the pressures around her.
Dempster knows that two key elements await her judgment. Firstly, does Butcher stay or leave? Secondly, can she distance herself sufficiently from Petrie, the man who appointed her, in order to assert her own authority on the club.
In regard to Butcher, Dempster sounded strong, but also cautious. It sounded like his future is not yet secured.
"I'll meet the manager next week, where we will discuss the direction we are going to take," she said. "I met Terry for the first time in his capacity as Hibs manager last week and emotions were very high. Relegation had just happened. So I have plans to meet Terry again and, once we've had that conversation, we will know more about the direction of the club. I can't say more at the moment, it's too early."
As for her relationship with Petrie, who will stay on at Hibs despite supporters' cravings to the contrary, Dempster could not have been clearer. "One of my concerns in coming here was, 'am I going to have the autonomy to go and do the job that is required?' Hibs have not had the best on-field results in the last couple of years. The club hasn't performed in the way it needs to.
"I wasn't going to walk away from a job [at Motherwell] where I had complete autonomy, and the absolute support of the chairman to go and do the job, only to walk into another post where my hands were going to be tied.
"So I've got the ball now. The responsibility is on me. The decisions that I make are the ones that are going to be judged.
"We have a tremendous infrastructure at Hibs but that is a bone of contention with supporters. We haven't had the team on the pitch. So it's my role to bring about a change in direction."
At Motherwell, various people speak extremely highly of Dempster's capability as a football executive. She is also said to be hands-on and likes to immerse herself in football issues, traits which might not always be to the liking of Butcher or any other manager, to judge by her comments yesterday.
"I've followed football for many years," said Dempster. "Here at Hibs we will take decisions collectively. Do I decide if certain players are signed or not, if a manager comes and makes a strong recommendation? Well, that is their judgment call. I need to make a decision on whether they are backed.
"In my previous post I met the players early - I had most of the dealings in that respect - and I don't see that changing."
The next two months, amid fan rebellion and acrimony in the air, will go a long way to shaping Dempster's destiny at Hibs. The club has had a calamity in relegation and faces a very uncertain 12 months ahead. Dempster, however, evokes a figure of conviction in this still very male-orientated environment.
"It's not just the football that needs to change here at the club," she said. "The non-football element needs to change as well. It's my job here - and my determination - to bring about a change in direction."