Recently, the stable operation of the upward thermal diffusion cloud chamber with respect to buoyancy-induced convection has become a concern in obtaining reliable nucleation data. During chamber operation, evidence of strong convective currents are clearly visible due to the curved trajectories of entrained droplets. A potential problem exists when these flows are much smaller in magnitude; there is no visible evidence of convection, yet these minute flows may result in systematic errors in the nucleation data calculated via 1D diffusive models of the transport mechanisms within the chamber. To examine whether such flows are possible and the characteristics of these flows we have developed an extension to recent 2D modeling of the nucleation chamber which includes buoyancy-induced, convective motion. We have examined both wet and dry chamber operation with an example case of 1-propanol in helium at a pressure of 1.18 bar. In addition, for the dry wall case we examined the effect of overheating the chamber wall and varying the chamber diameter. Results indicate that, for the representative cases investigated, very subtle convective flows can exist and that these minute flows can affect the maximum attainable supersaturation along the chamber centerline. Finally, a list of general recommendations are given for minimizing the possibility of such flows within the cloud chamber.