Although I am not familiar with this particular radio, I have seen many DC-DC inverters overheat and fail in VCR's. The main cause being electrolytic filter capacitors on the input and output side of the inverter. When these capacitors are heated for a long time, they begin to dry out and lose capacitance. As the capacitance goes down, the inverter draws more peak current and runs hotter. This dries out the caps even more and creates a thermal self-destruct cycle. I have seen DC-DC inverters in VCR's get so hot they even char the circuit board before failing.
Check if there is an electrolytic capacitor on the input and output of the inverter. Try replacing these and then recheck the inverter temperature.
73, de Tom, KA1MDAwww.ka1mda.org