>...and the properties of thermal paste (typically) are just barely better than air.
I am not certain how you have managed to come to such a conclusion. Thermal conductivity of air is around 0.03W/(m·K)[0]. Good thermal, non-conductive paste is like 12.5W/(m·K)[1] (or 400 times better than air). Conductive ones are in the region of ~40-80 W/(m·K) and Aluminium is 237W/(m·K). Also air also expands pushing the cooler and CPU away.
Normally you if choose between "too much" and "too little" paste, you pick the former. The pressure pushes out the unneeded amounts.
Don't, you need to multiply the raw conductivity by the linear distance occupied by the thermal paste? I presume that distance will be at least two orders of magnitude larger than that occupied by air in a metal contact only setup.
I would be extremely surprised if increased pressure due to air at higher temperature played any role whatsoever unless the bolts connecting the heatsink and cpu were very loose. If anything, I'd expect the increased conductivity of air at higher temperatures to dominate.
I'd also expect there to be effects at the metal-paste and paste-metal interfaces which reduce the effective system conductivity (i.e. phonons are much more likely to reflect in this scenario than in a metal-metal interface).
I am not certain how you have managed to come to such a conclusion. Thermal conductivity of air is around 0.03W/(m·K)[0]. Good thermal, non-conductive paste is like 12.5W/(m·K)[1] (or 400 times better than air). Conductive ones are in the region of ~40-80 W/(m·K) and Aluminium is 237W/(m·K). Also air also expands pushing the cooler and CPU away.
Normally you if choose between "too much" and "too little" paste, you pick the former. The pressure pushes out the unneeded amounts.
[0]: https://www.engineeringtoolbox.com/thermal-conductivity-d_42... [1]: http://www.thermal-grizzly.com/en/products/16-kryonaut-en