The temperature gauge responds to current, which depends on the voltage applied (between 12.5 and 14 volts) across the series combination of temperature sending unit resistance (variable, depending on temperature) and the resistance of the "broken" series resistor.

While the series resistor must be rated to dissipate the wattage (VČ/R or IČ*R, take your pick) at any current from cold to hot, this wattage rating will not really help you find its resistance.

So, we are back to the need to find the proper resistance value to get the proper replacement.

Now, if you know the resistance of the temp sending unit at gauge minimum and maximum temperatures (40C and 120C?) and amount of current it takes to drive the needle at these deflections, you can calculate the total resistance value and thus find your resistor value...