  We investigate the nontrivial interplay between geometry and temperature in
the Casimir effect for the sphere-plate and cylinder-plate configurations. At
low temperature, the thermal contribution to the Casimir force is dominated by
this interplay, implying that standard approximation techniques such as the PFA
are inapplicable even in the limit of small surface separation. Thermal
fluctuations on scales of the thermal wavelength lead to a delocalization of
the thermal force density at low temperatures. As a consequence, the
temperature dependence strongly differs from naive expectations. Most
prominently, thermal forces can develop non-monotonic behavior below a critical
temperature. We perform a comprehensive study of such geothermal phenomena in
these Casimir geometries, using analytical and numerical worldline techniques
for Dirichlet scalar fluctuations.
