  We consider topological entanglement entropy (TEE) at finite temperature for
CSS codes, which include some ordinary topological-ordered systems such as the
toric code and some fracton models such as the Haah's code and the X-cube
model. We find, under the assumption that there is no extended critical phase,
the finite-temperature TEE is a piecewise constant function of the temperature,
with possible discontinuities only at phase transitions. We then consider phase
transitions of CSS codes. We claim that there must exist a phase transition at
zero temperature for any CSS codes in 2D and 3D with topological order. This
statement can be rigorous proved for some familiar examples, while for general
models it can be argued based on the low-temperature expansion. This indicates
the break down of topological orders at finite temperature. We also discuss
possible connections with self-correcting quantum memory.
