Tank temp vs. room temp

I feel so bad. When I woke up yesterday morning the warm side temp was reading at close to 100 degrees, I quickly brought it back down and made sure my snake was moving normally. He isn't lethargic by any means and has a plenty large water dish, but he will not sit still! He's just bent on getting the hell outta here which is understandable since I almost fried him :/

Now I'm not sure how to keep his tank temps steady. It's been fine (pretty constant 90 degree warm side 80 degree cool and 50-60 prevent humidity) since I got him over a month ago, but we just got a bad heat wave here this week and I'm worried. I plugged up the ac vents in my room to keep his temps ok and I definitely wasn't expecting it to get that hot in there! Maybe if I cover the screen top with a towel I can just keep the ac vent open.

I'm using an infrared heat lamp right now maybe it's time to switch to a mat and thermostat.

Would I still have to worry about the ac or heater effecting the tank temp? My home is centrally controlled by a thermostat so I personally can't decide that the ac or heater just won't be on or how long.

Once you have a heat mat and a t-stat the temperature on the hot side will adjust itself and stay within proper range with little to no fluctuation.

The temp on the cool side on the other end will obviously fluctuate based on the ambient temp of you room.