You may paint it any color you like, it will still give you compost :)

Just thinking black would make things cook faster.

Mantis and other brands are painted (maybe manufactured is a better choice of words) green to better blend in with yards.

Having the tumbler exteriors in black would not significantly change the inside temp. The heat is generated inside the tumbler or bin, so those wishing to minimize heat loss would insulate the outside. Tumblers suffer in comparison to larger bins in winter composting -- there just is not the bulk to minimize heat loss.

I moved from a tumbler to two large mesh bins 4'x4'2'high years ago for a number of reasons.

I bought 2 mantis single barrel compost tumblers. Only 1 is still in service. I may use the other for spare parts if ever needed in the future. I have made my own out of 50-55 gallon blue plastic barrels. I made doors on the side with hinges that close and have a pole through the center. I have to spin it over the pole axle in the middle, kinda like on the price is right. you try and use your strength to spin it up and over on the big wheel. It works pretty darn good, despite the fact that the volume of organic matter isn't very massive, it rots pretty well, if given the time. It is easier to maintain even moisture.