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Your radio evidently has a heat-related electronics problem, though it is probably in the audio amplifier section rather than in the radio tuner.
I presume you have tried changing channels, when it is the radio that has gone silent, and gotten no better results.
Have you tried starting up the radio in a cold environment or after chilling it in a cold place e.g. a refrigerator, for 15 minutes almost to the minute (not too cold, in other words). (Note: do not freeze it, nor put it in a freezer - that would damage it for sure.)
If it produces audio longer that way, when started up chilled, that confirms a heat-related problem.
Check - just in case - that the Alarm (if it has one) is disabled.
How old is your Bose radio? measured from date of purchase.