We have calculated the temperature dependence of the frictional drag between spatially separated quantum wells with parallel two-dimensional electron gases due to interlayer electron-electron interaction mediated by virtual exchange of acoustic phonons due to piezoelectric and deformation potential interaction. It is shown that the frictional drag is dominated by the piezoelectric coupling. According to our calculations the temperature dependence of the drag scattering rate divided by T2 exhibits a pronounced peak that for the experimental situation and in agreement with the finding of Gramila et al., Phys. Rev. B 47, 12 957 (1993), is obtained at approximately T 2.1 K. We ascribe the appearance of this peak to a change from small to large angle scattering in the virtual phonon exchange.