@ThePhoton may copy stuff out of here into an answer as he sees fit if desired as it adds to his comment/answer. Copy out enough and I'll delete this answer.
M. Photon said:
The temperature isn't likely to change depending on rating. The fuse material will have a certain melting temperature.
The fuse wire will be sized to achieve that temperature at a different current, depending on the rating. So all fuses made from the same material will break at essentially the same temperature.
Why not estimate the rating by measuring the current through the fuse when it fails? That seems much more direct.
I more or less agree.
But its worse.
Fusing occurs when the metal wire melts BUT the construction will affect this significantly. The wire length will affect its thermal resistance from its hottest point. size of end caps, attachment to end caps etc will affect this too.
A manufacturer can probably achieve fusing over a 2:1 + ratio (just guestimating) with the same wire by changing thermal aspects such as wire nength, end cap attachment points and means, wire forming etc.
Wire material does vary with fuse type (I read). Some slow blows are said to use low temperature melting point alloys.
You could probably surface treat wire to affect its radiation effect. How much this affects fusingh compared with conduction to end caps i know not.
BUT, pointing an IR thermometer at fuses could be interesting and useful.
Note that the LASER used is for pointing guidance and that an IR sensor is used for temperature sensing. My experience is that with small targets the LASER pointing is useless and you can best locate hot spot by slowly "waving" sensor aperture to and fro on 2D over target. Also, background temperature (objects in same room) can make a large difference when target is small so screening may be needed.