  We give a model-independent derivation of general intersecting rules for
non-extreme $p$-branes in arbitrary dimensions $D$. This is achieved by
directly solving bosonic field equations for supergravity coupled to a dilaton
and antisymmetric tensor fields with minimal ans\"{a}tze. We compare the
results with those in eleven-dimensional supergravity. Supersymmetry is
recovered in the extreme limit if the backgrounds are taken to be independent.
Consistency with non-supersymmetric solutions is also discussed. Finally the
general formulae for the ADM mass, entropy and Hawking temperature are given.
