You can set the heat source to be in cells that are wet, or have some value of the liquid(solid) material. However, you can't then stop heat being convected/conducted into adjacent cells. Yes, the free surface may slow down heat transfer, but if you're adding it into a cell with some gas present you've already got hot gas.
Divergence can be caused all sorts of things. Check the mesh, source terms etc and review the flow & energy fields as the divergence occurs. That'll hopefully highlight what's going on.
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