Since the hypotermia mechanics has been developed to the point is its manageable and enjoyable, one would expect the other extreme should be also punishing and thus avoided.
Hyperthermia debuff should appear when one wears too warm clothes in a sunny day, stays near a fire for a longer period, especially near a finery forge, other metal industry structures and ovens. Lower mine levels should have slightly elevated temperature.
Also doing a lot of work, that is expending significant percentage of phlegm should cause short time overheating. That will significantly affect mining, using a forge, tending fields, digging soil, playing with animals and similar activities as well as running.
Sand biome on a sunny day should work as a counterpart of snow in winter.
Drinking water and glacier water, carrying snow or ice should temporarily remove hyperthermia. Though snow and ice melt now way too fast to be comparable to hot stones.
Hyperthermia should drain inspiration. At early levels it should simply negate natural inspiration gain.
It should also stop F&F timer so it is not reasonable to go to logout under hyperthermia for longer periods.
Hyperthermia may slowly remove Q&Q debuff, while being inferior to Mason Lodge facilities.
Untreated hyperthermia should lead to KO. To avoid KO loops both a leanto and a claim stone should provide some shade.
Frozen cape will become a reasonable choice for a number of activities.