The most general form of the problem of stagnation-point flow and heat transfer of a viscous, compressible fluid impinging on a flat plate is solved in this paper. The plate is moving with a constant or time-dependently variable velocity and acceleration toward the impinging flow or away from it. In this study, an external low Mach number flow impinges on the plate, along z-direction, with strain rate a and produces three-dimensional flow. The wall temperature is assumed to be maintained constant, which is different from that of the main stream. The density of the fluid is affected by the temperature difference existing between the plate and the incoming far-field flow. Suitably introduced similarity transformations are used to reduce the unsteady, three-dimensional, Navier–Stokes, and energy equations to a coupled system of nonlinear ordinary differential equations. The fourth-order Runge–Kutta method along with a shooting technique is applied to numerically solve the governing equations. The results are achieved over a wide range of parameters characterizing the problem. It is revealed that the significance of the aspect ratio of the velocity components in x and y directions, *λ* parameter, is much more noticeable for a plate moving away from impinging flow. Moreover, negligible heat transfer rate is reported between the plate and fluid viscous layer close to the plate when the plate moves away with a high velocity.