Three things to consider:
You should be able to touch the ceramic part of a heat lamp with your hands, if you can't then its gonna be WAY too hot in the cage for a snake.
Some people keep corn snakes at room temperature. There is literally nothing wrong with it as long as your house stays at a stable temperature and aren't feeding too often.
The typical heat pad doesn't get too hot to burn a snake or even really heat up a tank enough to cause problems for the most part as long as it isn't too big. Its even more rare for a failure nowadays that manufacturing/engineering of the common brands has gotten much better than in the past. Thermostats are a fail safe in all reality, actual temp control for a few people with specific temp issues based on their house or where they live. I used heating pads, like you for probably 10 years without ever having a thermostat. I never had a problem. The burned reptiles and such from heat pads/heat rocks are only the people who posted of a product failure. People who have a positive experience are much less likely to post a review or even talk about it. People who have something bad happen are MUCH MUCH more likely to post photos and stories and the like. I don't think the reptile burning was ever as prevalent as people think it was due to that. THAT SAID, everyone should have a thermostat for their pets that have heating elements because quite frankly it's not worth the risk and vet bills that would result from something like that. The 90's/early 2000's were the wild west of reptile keeping and not many people used thermostats at all, most of the reptiles got out just fine and I think that's part of the reason so many still don't use them or are even aware of them.