  We experimentally study the energy-temperature relationship of a harmonically
trapped Bose-Einstein condensate by transferring a known quantity of energy to
the condensate and measuring the resulting temperature change. We consider two
methods of heat transfer, the first using a free expansion under gravity and
the second using an optical standing wave to diffract the atoms in the
potential. We investigate the effect of interactions on the thermodynamics and
compare our results to various finite temperature theories.
