If there is significant temperature difference between indoor air and outdoor air, will that significantly increase the rate of air exchange?

There would be heat diffusion, of course, but heat diffusion occurs even without the exchange of fluid parcels between each environment.

We do know that cold air tends to be denser than warm air, and that pressure differences drive the exchange of fluid parcels. But let's assume that there is no pressure difference for the sake of this question.

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In Rayleigh-Bénard instability the fluid at the bottom is heated, this have for effect to decrease the density of the fluid at the bottom, when the gradient become strong enough the instability take place. So yes the fluid have larger density at the top and lower density at the bottom. Using the Boussinesq approximation, the relation used between the density and the temperature is $\rho=\rho_0 \beta T$ with $\rho_0$ the characteristic density, $\beta$ the thermal coefficient (negatif) and $T$ the temperature fluctuation. – aberration Nov 3 '12 at 21:02