Excellent point to discuss. There is no path to mechanical measurement without consideration of temperature differences and rate of thermal expansion.
Example of rates of thermal expansion in inches per degree F
Most ferrous alloys about 6.5E-6
Aluminum alloys 9.5 to 11.2 E-6
etc. Here's a handy table:
Thermal Expansion of Metals
All linear measurement is referred to 68 degrees F (20 degrees C), a world standard. Multiply your measurement by its rate of thermal expansion times the temperature difference ni degrees F. Metricoids, use the rates for the Metric world..
Post the expansion chart in your shop near near the surface plate or what passes for your inspection station.
You have to consider the temperature of the measuring instrument as well as the temperature of the part. Most measuring instruments (mikes, bore gages, etc are made of steel. If you handle a 4-5 outside mike and warm it 20 degrees F the frame will expand about 0.0006 affecting the accuracy of your measurement.
Another item to keep handy is a thermometer. For may years, I've used a dial type pocket thermometer like this
Taylor 5989N Stainless Steel Instant Read Pocket Thermometer
But now we have these remote reading infra red gadgets
Taylor 5989N Stainless Steel Instant Read Pocket Thermometer
which are very handy but may be plagued with petty emissivity errors.
There is no convenient path to precision in the home shop without consideration of temperature and thermal expansion and the necessary math for calculating its effects in precision measurement, clearances, interferences, etc.
Story: In my chip making days I was a specialist on large machine tools. One day working on a 10 ft vertical boring mill on a ring involving an inside diameter of 5 feet or so, I needed an inside mike to measurement. I had one prepared, ready for pick-up in the tools room's calibration lab. I sent my apprentice to pick it up and to handle it using thick wads of shop towels to insulate it from the heat of his hands. I'd already instructed him on the effect of temperature, walked him through the math of calculating expansion, why it was necessary to handle the inside mike to avoid uncontrolled heat transfer into it etc.
Imaging my shock when he returned down the long aisle not only bare handing a calibrated inside mike but using it like a walking stick, tapping the measuring tip on the concrete in time with every step of his left foot..
Sometime outrage outstrips the available profanity. I had to tell the boos there would be a three hour delay for re-calibrating the inside mike and why, suggesting a month in the sand blasters or tank cleaners (nasty jobs in a shipyard) as a reward for my errant apprentice. He got a week cleaning the chip troughs of the big shaft lathes which, in fairness, was at least nasty. My apprentice took his punishment in good heart and in time developed into a fine machinist.
Notice I tell no stories on myself. My apprenticeship was free of similar lapses. Trust me.