Referencing the '38-'39 Ford book by the EFV8 club, 1939 Standard cars used the fuse block, 48-12250, and 1939 DeLuxe models used the circuit breaker, 91A-12250. The circuit breaker is for the lighting system. The ballast resistor is the same for both models.
If you have a lot of current flow (lights on) then that box will get warm. It's a self-resetting thermal circuit breaker. Once too much current flows, it will pop, cool off and reset. In the meantime, you should get an indication (i.e. your light go out or flicker) that the circuit breaker popped.
It is possible the circuit breaker has failed and you have excessive current flow without it popping. Usually this condition is paired with another indication...usually smoke or fire as something shorts out.
Hope that helps.
COE Dan