The main concern of this paper is to investigate the effects on the stability behavior of wall suction or injection for external boundary-layer flow over a heated, porous plate for a fluid with temperature-dependent viscosity. The wall suction or injection are applied to the flow by a simple modification for the no-penetration condition and the current boundary conditions on the flat plate. Liquid-type viscosities are found to entrain both the velocity and temperature profiles closer to the plate with increasing both temperature sensitivity and suction intensity, whereas gas-type viscosities are found to exhibit the reverse effect with increasing flow injection and decreasing temperature dependence. We present then the linear stability analysis and find that increasing both the temperature dependence (from gas- to liquid-type behavior) and suction intensity of the fluid leads to increasing critical Reynolds number to a point of maximum stability. We note also that increasing both the Prandtl number (Pr) and flow suction in the liquid-type behavior results in an increased critical Reynolds number. The magnitudes of the perturbation eigenfunctions are considered before utilising them to obtain solutions to an energy balance integral. We find that the eigenfunction profiles are imitative of the narrowing of their mean flow counterparts when increasing either the temperature dependence or the flow suction. Our results are then confirmed by the energy analysis, where we find a significant reduction in the energy produced by the disturbance with increasing suction intensity and ultimately leads to a more stable flow. Overall, there is a strong destabilizing effect with increasing injection and the temperature-dependent viscosity over a heated plate. In summary, the findings indicate that increasing the wall suction and temperature dependence results in significantly more stable flows. It is worth noting that application and extension of this study are considered in the context of chemical vapor deposition reactors.