Page 110 of the DMG lists a DC 5 Constitution saving throw for "Extreme Heat" (temperatures of 100 degrees Fahrenheit or more). However, it doesn't make sense to me that it would remain the same as the temperature increases.
How do I fairly determine a DC for "Extreme Extreme Heat"?
Best Answer
As a DM, you have the authority to set DCs and other things and the game was designed expecting you to use this responsibility:
Since the granularity of weather extremes is obviously not important enough to the default game for it to bother with the complexity in the core rules, if you feel like it should be more granular, you should make it so. If you've got a sense that DC 5 once an hour is insufficient, that is the same sense you need to use to adjust it.
That said, since you're talking about extreme heat, not just extremely hot weather (the world hot weather record is "only" 134 °F), you may want to consider your room more like an oven that does direct damage every round or every few rounds, possibly with a saving throw, since 200 °F is literally an oven. A cool oven, but still an oven.
Post scriptum: You — or other readers — may be tempted to get engineer-y about the precise temperature — and if you and all your group enjoy that kind of realistic detail simulation, go for it. But if you're not, I advise not trying to calculate too carefully the precise effects of particular high temperatures, since the reality of heat management is quite complicated — and besides, D&D campaigns are more often in a genre were fighting on the lip of a pit of bubbling lava is non-lethal, making comparisons to real-world temperatures somewhat beside the point. Go with something fun and plausible that suits the amount of on-screen time this room will have, unless you're all into the details of thermal physics.