  Non-extremal intersecting p-brane solutions of gravity coupled with several
antisymmetric fields and dilatons in various space-time dimensions are
constructed. The construction uses the same algebraic method of finding
solutions as in the extremal case and a modified "no-force" conditions. We
justify the "deformation" prescription. It is shown that the non-extremal
intersecting p-brane solutions satisfy harmonic superposition rule and the
intersections of non-extremal p-branes are specified by the same characteristic
equations for the incidence matrices as for the extremal p-branes. We show that
S-duality holds for non-extremal p-brane solutions. Generalized T-duality takes
place under additional restrictions to the parameters of the theory which are
the same as in the extremal case.
