Yooo! Thanks a lot for the comment! It was pin point! It's based on Wario World and Dumb Ways to Die. Now, regarding your question, let me go nerd mode:
We didn't have enough time but we wanted to change more stuff with the increasing Difficulty value but at the end we could only use it to affect spawnrate. It's a logarithmic function with diminishing returns, 66% as expected by minute 1, 100% by minute 2 and 133% by minute 3, 500% by 1h.
Now, the core's heat goes from 20% to 80% and stalls there by minute 2. That means 1 valve should be enough HOWEVER, every minigame you fail increases 3% the core's heat, making it so past 7 misses and 2 mins, 1 valve won't cut it and you'll be forced to handle both.
Technically, as the spawnrate becomes infinitely shorter, that makes it physically impossible to fix every minigame. Making it so core heat passes 200% with a total of 40 misses and 2 minutes, past that point you are gone for as 2 valves sum up to 200% coolant. Tho you'll probably die before that, as minigames take time to handle and valves lose speed independently.