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Depending on how you set the source you may find the refinement just adds the source into a smaller volume (cell) which means the temperature gradients are still not resolved unless you further refine the mesh which could again add the source into a smaller cell etc..... Â
How often are you updating the source positions? An alternative option could be to split a cell(s) out after meshing and then add the source to the new cell zone. You can adapt in that region without changing the source as volume as it's a zone rather than a cell. Have a look at mesh separation, and you can do that using a register (in the adaption tools).Â