As in the presented case natural convection will occur (density-temperature dependence), one simple equation for the temperature profile is not available. Moreover, the presented case will be time-dependent, so the profile will be changing with time.

However, you can do some CFD simulations (2D, transient) in order to calculate the temperature profile.

Thanks Jan. I tried a simulation, although keeping the density constant for initial results but the profile looks promising. Obviously as expected, Twall1 being higher, the peak temperature as seen in progressing time steps always lies in the region closer to Twall1.

You might want to start with an easy problem that can be easily solved without the need of complicated/expensive software to get some insight into the type of convection pattern you might observe. That is convection in the plane which occurs when your end wall of your container are far apart relative to the spacing between the side walls. The steady planar flow is described by the following non-dimensional equations ( when Re