  We point out the presence of a $T \to -T$ temperature-reflection
($T$-reflection) symmetry for the partition functions of many physical systems.
Without knowledge of the origin of the symmetry, we have only been able to test
the existence of $T$-reflection symmetry in systems with exactly-calculable
partition functions. We show that $T$-reflection symmetry is present in a
variety of conformal and non-conformal field theories and statistical mechanics
models with known partition functions. For example, all minimal model partition
functions in two-dimensional conformal field theories are invariant under
$T$-reflections. An interesting property of the $T$-reflection symmetry is that
it can be broken by shifts of the vacuum energy.
