Furnace/thermostat question

So, people who have gas heaters, enlighten me. My boys' room is on the same circuit as the furnace, I am told, a circuit that randomly flips off, even in the summer. The boys lost power last night, as we discovered when my son didn't get up on time for the substitute newspaper thing he's doing. So you could say that the reason it was only 63 in the house when we got up instead of 68 as set by the thermostat was because the heat was off for an unspecified amount of time. But...it's just past noon, and it's only made it up to a whopping 64. The heat's come on once in the past hour. We have a well-insulated house and the newish windows are all shut. It's 36 and sunny outside, so not terribly cold for this place (it can get down to -20). Naturally, it's the day after Thanksgiving and everyone is on holiday except for retailers; there's not even a way to reach an emergency maintenance number at the property manager except for leaving messages on their regular maintenance message service (phone and e-mail). It's not like there's NO heat...but it's not like it's doing the job properly, either. Suggestions? I really don't want to call emergency maintenance heating people out on a holiday weekend if all they're going to do is tell me it's in my head...but I don't want to freeze, either. I even thought maybe we just need to change the filters, but no matter how many times I've searched, I've found neither filter nor place to put one. (!!!) (There are some places in the walls that look like air intake grills, but they are permanently painted shut/screwed in with 3" screws. And nothing around the actual furnace that I can see.)

I actually have a sore throat and am tired from driving said kid around before dawn to deliver papers. I would rather take a nap than worry about heater people calling me back. Has anyone here dealt with a sub-functioning heater before?