The development of a heat-transfer and of a two-dimensional viscous incompressible flow generated from a deformable circular cylinder impulsively started into rectilinear motion is studied numerically for a wide range of Reynolds numbers (Re = 550-9500). The vorticity transport equation and the energy equation are solved by a second-order finite-differences method in both directions of the domains. The Poisson equation, for the stream function, is solved by a Fourier-Galerkin method in the direction of the flow that we assume to remain symmetrical, and a second-order finite-difference for the radial direction. The advances in time are achieved by a second-order Adams-Bashforth for Re = 550-3000 and by a fourth-order Runge-Kutta for Re greater than 3000. The computed results are compared qualitatively with experimental and numerical,results done before in the particular nondeformable case. The comparison is found to be satisfactory.