A special case of Falkner–Skan flows past stretching boundaries is considered when the momentum and thermal slip boundary conditions are allowed at the boundary. Exact analytical solutions are found for the converging channel (wedge nozzle). The solutions are shown to be unique, double, or triple depending on the slip parameter and wall moving parameter. The provided closed-form analytical solutions are rare class of exact solutions for the Falkner–Skan flow equations. Thresholds of existence of multiple solutions are determined. For each flow solutions, the corresponding energy equation is also exactly solved when the internal heat generated by viscous dissipation can be neglected or numerically integrated when the viscous dissipation is significant. Analytic and numeric values of the rate of heat transfer affected by the presence of a surface temperature jump are also worked out. The possibility of realistic physical solution out of multiple solutions is finally discussed.