The size of the fuse will not affect the relay as far as it getting hot. By the way is the relay getting hot? If it is something is not wired correctly
So exactly how did you wire this? I would think you would take the wire from the stock horn, connect it to terminal #85 of the Hella relay coil, ground terminal #86 of the coil, run a fused wire from the battery to terminal # 30 on the relay then from terminal 87 to the air pump and ground the pump? If this is how it's wired and it stays on then it has got to be the relay. If it's not wired that way could you provide a description of how it is wired?