I-V curve of resistor in special condition
I model resistors based on their physical size, assuming the core of the resistor is pure silicon.

As I computed in a recent answer, a resistor with 1 cubic centimeter volume will heat up about 1 degree centigrade per second, for each watt of power dissipated.

A resistor of 1/10th the size inn each dimension, or 1/1,000 the volume, will heat up 1,000X faster or 1,000 degree centigrade per second. Thus a 1mm^3 cube resistor will heat up at 1,000 degree C per watt per second.

However, with the thermal timeconstant of 1mm^3 of silicon being  0.0114 seconds ( down from the 11,400 seconds for a cubic meter of silicon, or 1 Milliion X slower ), the 1mm resistor heats up and starts to dump heat out the solder joint into the copper traces on the PCB. Should you be interested in further thermal modeling, standard copper foil (1 ounce/square foot, 35 microns thick, or 1.4 mils thick, 0.0014") has 70 degree  Centigrade per watt as the thermal resistance, for any size square of that foil.

Decades ago some newly minted techs asked me about overheating. We placed a 4.7 ohm resistor of rating 1/4 watt, across 5 volt supply.

** the resistor flared to fire in about 2 seconds. **