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If the tab and stud have equal heat conduction from them, yes, the whole diode will heat to the same temperature. That is the whole reason for having a stud, it is to allow better heat conduction to a heat sink.
If you are concerned about the tab temperature, it will probably be hotter than the stud in most situations but not by much. The actual amount depends upon how much heat is dissipated by the tab into wiring and the environment. DO-5 diodes are designed so the majority of heat is conducted directly or through the body filling to the stud.
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