Whatever you do, don't just put in a bigger fuse. Under the best scenario, you've got no. 12 wire running the circuit. that's good for 20 amps. what is much more likely is that it's no. 14 wire, good for 15 amps. In most places, if you have a fuse box rather than breakers, the circuits were designed as 15 amp circuits. In the era that fuses were the standard equipment, we didn't have as many electrical items in the typical home, so 15 amps were the standard size circuit. As time marched on, we tend to have more electrical load in our homes so 20 amp circuits became the standard. The problem is people got used to the idea that when you overload a 15 a circuit, just screw in a 20 amp fuse and everything is kosher. In reality what happens is that if you are wired for 15 amps but continuously pulling more than that through your wiring you will eventually get thermal breakdown of wire insulation or other components.
Not to bore you with the details, but to give you an understanding of the risks involved, pulling more than 15 a begins to overheat the wire and insulation beyond it's safety factor. As the wire heats up, the resistance of the wire also goes up. As resistance increases, it requires more amprage to overcome the resistance of the wire and still deliver the required amount of amprage the equipment is calling for. This is a vicious cycle that sooner or later will lead to a failure and under many circumstances, an electrical fire. 9 times out of 10 when you hear of a fire that started electricaly, this is the cause.
On a side bar, reguardless of wire size, I would inspect the wire leaving the fuse box. If it's not plastic or rubber coated and by that I mean, it looks like it's coating is made of string woven around the conductors, I would de-rate my load by 25% of the rated wire size, minimum. Over the years, I probably removed several miles of this type of wire and I can say with authority that it is not uncommon at all for that type of insulation to be so brittle from thermal breakdown that it crumbles from handeling. Be cautious if you decide not to replace this type of wire.