Another thing to keep in mind is that at equilibrium, you have thermal excitation everywhere. You might as well ask why you don't hear or see or smell the thermal excitation in your own brain.
I think you are suggesting something like: if I was detecting thermal vibration by the vibration of a membrane due to thermally induced air pressure I wouldn't because the temperature is the same in the air on both sides of the membrane and therefore the thermal air pressure on each side of the membrane is the same and so fails to move the membrane. If this is what you are suggesting it is wrong, and in a basic enough way to merit explanation.
Sound is pressure changing in time. Thermal vibration follows a random distribution. The air on each side of a membrane at the same temperature will have the same statistics of pressure change on each side of the membrane, but not the same instantaneous pressure on each side of the membrane. If the random pressure exceeds p1 25% of the time an is less than p0 25% of the time, then 6.25% of the time there will be a pressure difference of at least p1 - p0 on the membrane, and a different 6.25% of the time there will be an opposite sign pressure difference of at most p0 - p1 where we have chosen p1 to be the higher pressure than p0. So thermal vibrations will absolutely cause a membrane to vibrate randomly. Further, it is the case that the magnitudes of p1 and p0 rise as temperature rises as temperature rises, so we expect the membrane to be moved more when surrounded by hotter air than it does when surrounded by cooler air.
SO it is the case that generally heating air makes its average pressure rise if it is in a constrained volume, and a membrane will certainly not be displaced on average if it has air on each side at the same average pressure, but it is the temporal or time variations that produce sound, and the time variations on each side of the membrane for most conditions you can create in the lab are uncorrelated, and so the membrane vibrates randomly and with an amplitude that rises as the temperature of the air rises.
I don't make that suggestion at all. I'm pointing out that sound receptors are just neurons, and if the thermal vibrations in your ear can excite some set of neurons than the thermal vibrations impinging on the dendrites of any neuron in your body - including inside your brain - should also elicit a response.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.