I'd install a 50A or even 60A fuse then. Fuses are meant to be protection against catastrophic failure and not affect the circuit under normal operation, nor are they meant to run near their fuse value. Upping the value a little won't hurt the protection at all and will not be so hot - that is if the heat is coming from the fuse itself and not the connectors/wiring.
However if the fuses are the ATO/ATC type, 40A is the max size available IIRC and would have to replace it with something a little larger, like a
mini-wafer fuse (the larger ones are just too darn big). Or I suppose you could parallel a couple 30A ATC fuses/holders.