It's pretty common for a CMM to be in its own climate controlled room. Parts will be placed in the room and allowed to reach reference temperature for a several hours prior to measurement.
On production lines you usually skip the absolute measurement of a CMM and use go/no-go gauges. One should fit, one should not. They'll be made of a material with similar thermal expansion coefficients as your parts. As long as they've both been sitting around for a while they'll be at the same temp. They'll have expanded or contracted the same amount from reference so their relationship of go/no-go will still hold true.
The whole field of metrology is a never ending rabbit hole - really interesting the more you get into it.