I would think it depends on the material being tested, like the crystal grain structure, orientation and dimensions. Consider a pure single crystal facet of copper. Indenting its face will cause heat to be transferred faster in one dimension vs. the perpendicular direction. If you are looking for any response to affect drift it would correlate to the crystallinity and conductivity of the material and therefore correlate to its annealing property. I'm not sure of what is your goal.
I guess Aditya is talking of the thermal drift related to the indentation testing machine. When experiments last a given amount of time, some slight changes of the environmental temperature induces some dilation/retractation of the components of the testing machine, leading to a drift on the measurements (a sort of thermal displacement). This effect is clearly visible for displacement controlled experiments.
Actually, I do not have the answer. Manufacturers have their own correction strategy (that is sometimes not detailled). You should ask the company who built the device you use what is the recommended way to correct these drifts.