1. Assuming your talking 0.001", not mm?
2. Assuming you're talking deg F, not deg C?
Could be possible, but unlikely at those toloerances. +/- 0.001" is quite lose.
To give you an idea how temperature affects stuff, a 100mm iron rod will change in length by 0.012mm at a temperature change of 10 dec C. (source= Mitutoyo Engineers Reference Book, page 11).
The Machinery's Handbook gives a more detailed analysis (page 405) the thermal co-efficient of expansion affects it too.
I would suspect the spindle changing length as it warms up (you do perform a warmup cylce with the coolant running?)
Could also be coolant changing temperature, if used. All these can be monitored and managed.
I run the aircon 24/7 in my lab so that the machine can temperature soak. My compressor also runs 24/7 for the same reason. My spindle is liquid cooled again to stop temperature effects.
Temperature is my enemy. Don't even get me started on humidity lol
Oh, also, remember that if you're cutting a hole, say for example boring a hole, the hole will expand as it heats exactly as if the hole were a disk of the same material.