  We present measurements of microwave-induced Shapiro steps in a
superconducting nanobridge weak link in the dissipative branch of a hysteretic
current-voltage characteristic. We demonstrate that Shapiro steps can be used
to infer a reduced critical current and associated effective local temperature.
Our observation of Shapiro steps in the dissipative branch hows that a finite
Josephson coupling exists in the dissipative state and thus can be used to put
an upper limit on the effective temperature and on the size of the region that
can be heated above the critical temperature. This work provides evidence that
Josephson behaviour can still exist in thermally-hysteretic weak link devices
and will allow extension of the temperature ranges that nanobridge based single
flux quantum circuits, nanoSQUIDs and Josephson voltage standards can be used.
