It starts with the water, not the air
The common musk turtle lives in slow streams, ponds, and swampy backwaters across eastern North America, and it spends nearly its whole life in the water — walking along the bottom more than swimming through it. So when keepers ask about temperature and humidity for this species, the honest answer is that water temperature is the dial that matters: hold the water between 72 and 78°F, using a submersible heater guarded against a curious turtle if your room runs cool. Humidity in the usual reptile sense needs no managing at all above an open or mesh-topped tank, because a water-dwelling turtle carries its moisture with it.
A basking spot it will actually use
Offer a basking platform — a piece of driftwood, a floating dock, or a sloped rock — with the surface warmed by a basking lamp to about 85-90°F at shell height. Musk turtles are shy, secretive baskers compared with sliders and painted turtles, and many keepers rarely catch theirs out of the water, but the option still matters: brief dry-off periods under a UVB lamp help keep the shell and skin healthy. Position the lamp over one end so the far end of the tank stays a few degrees cooler, giving the turtle a mild gradient to move through during the day.
Shallow water for a weak swimmer
Depth is a temperature-and-safety issue in one. Musk turtles are poor swimmers, and juveniles especially can tire and struggle in deep water. Keep the depth modest — roughly one and a half to two times the turtle's shell length — and provide plants, wood, and resting ledges it can cling to on the way up to breathe. That shallowness also keeps the whole water column close to one temperature, so the turtle is not chilled each time it sinks to the bottom to forage among the leaf litter and substrate where it prefers to hunt.
Air above the water, and warning signs
The one air detail worth attention is drafts: a tank sitting under an air-conditioning vent or beside a cold window exposes the turtle to chilly air each time it surfaces to breathe, and repeatedly breathing cold air over warm water is a classic setup for respiratory trouble in aquatic turtles. Move the tank out of drafts, and watch for the signs — swimming lopsided, frequent yawning or open-mouth breathing, bubbles at the nose, or a turtle that stops eating in water you have verified is warm enough. Those signs mean a reptile vet, promptly. Putting the weekly partial water changes, heater checks, and basking-lamp inspections on a KinsLe Care Teams list keeps this turtle's quiet, watery world verified on schedule, with every completed check marked by its timestamp.