  The heating of a two-dimensional electron gas by an rf electric field
generated by a surface acoustic wave, which can be described by an electron
temperature $T_e$, has been investigated. It is shown that the energy balance
of the electron gas is determined by electron scattering by the piezoelectric
potential of the acoustic phonons with $T_e$ determined from measurements at
frequencies $f$= 30 and 150 MHz. The experimental curves of the energy loss $Q$
versus $T_e$ at different SAW frequencies depend on the value of $\omega
\bar{\tau}_{\epsilon}$, compared to 1, where $ \bar {\tau}_{\epsilon}$ is the
relaxation time of the average electron energy. Theoretical calculations of the
heating of a two-dimensional electron gas by the electric field of the surface
acoustic wave are presented for the case of thermal electrons ($\Delta T \ll
T$). The calculations show that for the same energy losses $Q$ the degree of
heating of the two-dimensional electrons (i.e., the ratio $T_e/T$) for $\omega
\bar{\tau}_{\epsilon}>1$ ($f$= 150 MHz) is less than for $\omega
\bar{\tau}_{\epsilon}<1$ ($f$=30 MHz). Experimental results confirming this
calculation are presented.
