The electrical resistance of a percolating medium- made of A polymer f
illed with conductive particles may undergo a steep increase over a na
rrow temperature range above room temperature. A likely mechanism for
the effect is the loss of interparticle contact inducing a weakening o
f the connectivity of the medium as temperature is increased. When Jou
le heating is used, the sample behavior depends strongly on whether a
tension or current source is used. We show that in the first case, at
any value of the voltage drop across the sample, a stable state is rea
ched; on the contrary when a convenient exciting current is used, the
sample resistance may diverge spontaneously with time. We demonstrate
that most of these behaviors are compatible with the predictions of a
random thermal fuse model.