Ok let me explain this a bit.
Yes, the wattage affects the temperature. A 50 watt resistor can dissipate more heat than a 25 watt resistor. The higher wattage resistor will not get so hot. The actual temperature calculation is a bit out of scope.
Lets do some resistor calculations.
Look up the bulb you are replacing here, to find out what wattage it draws:
https://en.wikipedia.org/wiki/List_of_automotive_light_bulb_types
In this example, we shall be replacing a standard 3757A. I will do the math for higher filament.
Let us stick with the 27w turn signal/brake filament.
Take 27 w and divide it by 12. You get 2.25 amps. That is how much current the 3757A turn signal filament requires. A typical switchback lamp draws about .280 amps. That means you need a resistor that can pull something close to or just a little less than 2 amps to make the LED lamp appear to be a standard 3757A Let us do the math. 2 amps = 12 volts divided by 6 ohms. So how much wattage will that draw? Let us see 2 amps times 12 volts = 24 watts. I bet it will work file with an 8 ohm resistor, but a 6 ohm is more common, and ideal. Anything between 6 and 8 ohms will work.
Now what about heat? Well if we are only talking about the turn signal circuit, the lamp is on for about 240 ms, and off again for about 240 ms (50% duty). A 50 watt resistor is mostly aluminum, and has a mass of about 30 grams. Without going into all the math, it will reach a free air temperature of less than 32 c if left on all day. However if the lamp is doing double duty as a brake lamp, the resistor will be dissipating far more heat while your foot is on the break, and may easily exceed 50 c. Better fasten it down to some metal.
A three ohm resistor will draw 4 amps (12 volts / 4 ohms = 4 amps). 12 volts times 4 amps is 48 watts, and that is very near the maximum the resistor can dissipate. It better be attached to some metal.
Here are the simplified formulas ( for non engineers):
Wattage = Voltage * Amperage
Wattage = Amperage * Ohms suqared
Amperage = Voltage / Ohms
Amperage = Wattage / Voltage
Voltage = Ohms * Aperage
Voltage = Wattage / Amperage
I can work the math on some others if you like.
I know someone will ask about the 7443NA, so I will do the math on that one as well. The turn signal filament draws about 21 watts. That means the filament draws 21 divided by 12 volts or 1.75 amps. Again the switchback will draw about .280 amps. An 8 ohm resistor will be ideal, but a 10 ohm will also work. 12 volts divided by 8 ohms comes to 1.5 amps, or 18 watts. The combination of your switchback and an 8 ohm resistor will appear to be exactly the same as a 7443NA. The total wattage will work out to 21 watts. At a 50% duty cycle, a 50 watt resistor will reach only about 28 c, and that is car cooler than the air under your hood.