If you have a periodic structure illuminated by plane source, you need to use periodic BCs. However, if you have an isolated device you will need to use PML BC with TFSF source surrounding your device. I thought that you have periodic device and that was the reason why I used periodic BCs. Please note that if you use plane source with PML BC, you will get artefacts called edge effects.
In your first plot, since the temperature is almost similar (300 K) all over device, the plot will not be precise. I recommend using a bigger scale factor (when you import absorption profile into heat solver) to better resolve the heat distribution profile. Part of problem can be also because of the coarse mesh which I explained below.
Regarding the weird sphere shape, I guess it is coming from course mesh. You can increase the mesh resolution in Device as is shown below:
Make sure that you have checked the box and you are using fine enough mesh. Then mesh the structure and visualize grid before running simulations to make sure that you have set it correctly.
The other thing is that simulating a periodic structure in Heat solver is not straight forward since your thermal simulations does not have periodic BCs. One workaround is to do convergence testing in which you start with one unit cell and run both optical and heat simulations to capture temperature profile. Then increase the number of unit cells and repeat the simulations until your temperature profile remains unchanged in the central unit cell. The heat profile in central unit will represent temperature distribution all over the geometry if you had periodic BCs.
I hope this will help you solve the problem.