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 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).