How does a fuse resistance vary with temperature change?
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.