  Starting from the Lifshitz formula for the Casimir force between parallel
plates we calculate the difference between the forces at two different
settings, one in which the temperature is $T_1=350$ K, the other when $T_2=300$
K. As material we choose gold, and make use of the Drude dispersion relation.
Our results, which are shown graphically, should be directly comparable to
experiment. As an analogous calculation based upon the plasma dispersion
relation leads to a different theoretical force difference, an experiment of
this kind would be a decisive test. We also present an analogous calculation
for the case when the two plates are replaced with a sphere-plate system, still
with gold as material in both bodies. The sphere is assumed so large that the
proximity theorem holds. Discussion of the consistency with the third law of
thermodynamics and the validity of the surface impedance approach is provided.
