  Anomalously high and sharp peaks in the conductance of intrinsic Josephson
junctions in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) mesas have been
universally interpreted as superconducting energy gaps, but here we show they
are a result of heating. This interpretation follows from a direct comparison
to the equilibrium gap, $\mathit \Delta$, measured in break junctions on
similar Bi2212 crystals. As the dissipated power increases with a greater
number of junctions in the mesa, the conductance peak abruptly sharpens and its
voltage decreases to well below 2$\mathit \Delta$. This sharpening, found in
our experimental data, defies conventional intuition of heating effects on
tunneling spectra, but it can be understood as an instability into a
nonequilibrium two-phase coexistent state. The measured peak positions occur
accurately within the voltage range that an S-shaped backbending is found in
the {\it calculated} current-voltage curves for spatially {\it uniform}
self-heating and that S-shape implies the potential for the uniform state to be
unstable.
