Yes, depending on the temperature the emission can be anywhere in the electromagnetic spectrum. Check out this graphic from NASA and the Harvard-Smithsonian Center for Astrophysics:

As you suggest, when an object cools or heats the kinetic energy of the atoms decreases or increases (respectively), and the peak of the radiation shifts. Note that what is listed on the graphic above is just the peak wavelength. For example: stars like Eta Carinae have temperatures well above 10,000 K and thus have peak emission in the ultra-violet range. Yet Era Carinae also radiates a lot of visible light and in fact is possibly visible to the naked eye with a magnitude of 6.2.

Yes, depending on the temperature the emission can be anywhere in the electromagnetic spectrum. Check out this graphic from NASA and the Harvard-Smithsonian Center for Astrophysics:

As you suggest, when an object cools or heats the kinetic energy of the atoms decreases or increases (respectively), and the peak of the radiation shifts. Note that what is listed on the graphic above is just the peak wavelength. For example: stars like Eta Carinae have temperatures well above 10,000 K and thus have peak emission in the ultra-violet range. Yet Era Carinae also radiates a lot of visible light and in fact is possibly visible to the naked eye as it has a magnitude of 6.2.