From your earlier posts you have a '79 Shadow II in which case the thermal fuse is mounted on the alternator bracket. It's the black plastic rectangular block which as three thick cables connected to it.
It serves a dual function, Firstly it contains a fusible link that would blow instantly if the compressor clutch coil, or cable between the coil and the fuse were to short. The third connection goes to the superheat switch mounted in the back of the compressor. When this grounds, for example when the refrigerant is low, it causes a resistor mounted next to the fusible link to gradually heat up. If this happens for an extended period the heat generated melts the link cutting the supply to the compressor clutch. From your description this is possibly what has happened.
If I recall, the three connections are marked S, B & C and correspond with connections to the superheat switch, battery (supply or input) and compressor clutch.
Its purpose is to protect the compressor against a low refrigerant charge that would cause compressor damage. Under this condition it would heat for extended period as the superheat switch provides a constant ground. Transient conditions, that are not damaging to the system, however do not allow the resistor to get hot enough to melt the fuse.
The gradual heating of the resistor should differentiate between the two however there was a factory modification that involved adding yet another resistor in series with the first that extended the heating time even further.
Like all fuses it can be jumped and a plastic Littelfuse can be used to bridge between the incoming supply current to the clutch feed, B & C. This provides protection to the clutch but obviously bypasses the superheat protection.
OE thermal fuses are quite expensive and difficult to get hold of but aftermarket ones are easy to order on line and in my experience are just as reliable and only 1/10th the price.
You sometimes see cars where a new original type fuse if fitted thermal protection is made ineffective by disconnecting the round push on connector to the superheat switch on the rear of the compressor. It's a good indication that someone's trying to hide a problem.