Two dimensional, buoyancy induced wall plume flows near a corner are investigated numerically. The Navier-Stokes and energy equations are solved to monitor the flow behavior for different plume source locations and heat input. Observations are made of the plume propagation rate and transient temperature variations downstream the source. An interesting observation is how the initial bulk of fluid next to the plume source moves downstream. After a short time of pure conduction, this fluid starts to rise with a vorticity that causes it to expand along the normal direction to the wall. As a result, as the initial bulk of heated fluid flows downstream, at any given location, the local temperature maximum gets farther away from the wall. The focus of this article is to find interpolative functions to report and analyze the transient flow and relate some of the observations to plume heat input and location. These functions can be used in the designing phase of various industrial applications such as a data center with heat dissipating electronic devices. Another applicable area for these functions would be the inverse heat transfer or fluid flow problems where by measuring a few parameters downstream of the flow, the plume source heat input and location can be found.