@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.
The current rating of a fuse represents the minimum sustained current the fuse will blow at ... eventually. A 1A fuse will take 1A for a very long time without blowing, and if the fuse can dump some heat into the PCB or has airflow across it, may never blow at 1A.
The critical parameter is the \$I^2 \cdot t\$ rating, which gives you an idea of the energy (power and time) needed to blow it. (Remember that fuses are really meant to protect circuits when there are catastrophic failures.)
It's crucially important to match \$I^2 \cdot t\$ ratings, since if you replace a fast acting fuse with a slow-blow type, even thought they both say 1A, it's going to take radically different energy levels to actually blow them.
When the fuse is intact, you only have an \$I \cdot R\$ voltage drop across it. This drop is going to be nowhere close to the voltage rating of the fuse (else it acts like a big resistor and limits the energy available to your circuit.) Once the fuse blows, the voltage rating comes into play, which represents how much voltage potential the open fuse can withstand without flashing over and re-energizing the compromised load circuit.
Best Answer
Yes, hot resistance will generally be higher than cold resistance. And it will be higher at higher ambient temperature.
A decent fuse datasheet will list the cold resistance and the hot voltage drop at room temperature. You can calculate the hot resistance by dividing the voltage drop by the rated current.
Normal operation will likely be somewhere between those two values.
For example, a GDC-1A Buss fuse has a voltage drop of 87.5mV typical at 20°C Ta and 1A, so the hot resistance is 87.5m\$\Omega\$. The cold resistance is typically 75.7m\$\Omega\$.
Sometimes a figure is quoted as a ratio of hot to cold.