Although we don't usually go around feeling them, I think it inevitable that any fuse will get quite warm when the current flowing through it is approaching (or at) the 'rated current' of the fuse. Don't forget that one would normally expect the fuse to rapidly blow with less than double the rated current flowing (hence less than 4 times the power being dissipated in the fuse as compared with when it is carrying it's 'rated' current) - and by that stage it is so hot that the metal of which it is made melts.I will let others discuss whether that is normal or not. Just never noticed a 13A fuse with a =<10A load getting warm myself.
Of course, I'm talking about the temperature of the fuse wire itself. That will normally be surrounded by sand (or similar) and a ceramic casing, so the touchable outside of the fuse will be fairly well thermally insulated from the fuse wire. However, if the high current flows continuously, the outside of the fuse will eventually get pretty warm.
Kind Regards, John