Non-extremal Intersecting p-branes in Various Dimensions

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.