Despite the challenge description and title, no, there isn't any temperature change gimmicks.
This week's cup, Fire and Ice is all about microgames that change scenery between hot and cold alternatively. Luckily, it seems the set order of Week 1's cup returns (albeit with a different microgame set), so it should be possible to master the microgames with some practice.
I got a score of 1,724 using Jimmy T and 5-Volt, chars that had a high enough score while not being literally uncontrollable. Maybe once I master the 14 microgames on display, I'll be able to play higher scorers such as Kat.
Edit: Looks like I won't have to, however. Got a score of 2,709 despite a couple false starts with the same crew. Was finally able to move to Better Mortal status too.