  We have developed a method to probe the temperature of surface state
electrons (SSE) above a superfluid Helium-4 surface using the Seebeck effect.
In contrast to previously used SSE thermometry, this technique does not require
detailed knowledge of the non-linear mobility. We demonstrate the use of this
method by measuring energy relaxation of SSE at 1.6 K in a microchannel device
with $0.6\:\mu\mbox{m}$ deep helium. In this regime, both vapor atom scattering
and 2-ripplon scattering contribute to energy relaxation to which we compare
our measurements. We conclude that this technique provides a reliable measure
of electron temperature while requiring a less detailed understanding of the
electron interactions with the environment than previously utilized thermometry
techniques.
