There is no standard that I know of. You are correct in that it will vary from piece of equipment to piece of equipment. What has to happen is the components that comprise the pickups need to reach standard temperature. (Or close to it).
For example: On a CMM the thing that is doing the measuring is usually a glass piece with graduations etched on it. This piece of glass would need to come to standard temperature to take all the variation due to temperature (expansion/contraction) out of the equation. So you could check this by using a pyrometer and shooting the piece. Which, of course, is NOT readily available for direct viewing always. (One would think they would wire this in to the CMM, I mean, thermocouples are relatively cheap). This could happen quickly or take quite a long time depending on the object. It's a heat transfer question.
You could test it by measuring something AT STP in the lab and looking at the error. Example: If I have a 1" gage block in the lab and I know it's at STP because it has been in the lab for weeks, and I measure this and get 1.001", it could be the thing I am measuring with hasn't soaked long enough. It could also be error in the device.
In truth, because the heat transfer has an asymptotic boundary, it will take an infinite amount of time for the object to reach the "same" temperature as the lab. So the reality is you only have to wait until the error is "good enough." That depends on what you are measuring. Are you making 2x4s or bearings?