Berkeley SPICE allows you to define different models for resistors. In the model card, the temperature dependent behavior is defined by three parameters,
TC1 is the first order temperature coefficient and
TC2 is the second order coefficient.
TNOM is the nominal temperature at which the parameters have been measured.
The resistor value at a specific temperature is given by
To make a resistor conform to a certain model, you need to specify the model name in the resistor card:
RXXXXXXX N1 N2 <VALUE> <MNAME> <L=LENGTH> <W=WIDTH> <TEMP=T>
<MNAME> is the place to specify the model.
Other SPICEs have similar capabilities. Check your documentation for the specific syntax for your SPICE.
Note that none of this implies that SPICE can simulate self heating. You will need to specify the temperature of the device in either a
.OPTIONS card or in the
<TEMP=T> field of the resistor card, and that value will be used to determine the resistance.
I notice you actually specified Altium's SPICE. Altium apparently has a very similar set of paramters to Berkely SPICE, but you should specify them in a model file, rather than a .MODEL card.