Triac power dissipation
The resistor value does not noticeably affect the power dissipation. It only conducts briefly at the beginning of each cycle until the current is sufficient to trigger the gate. Using an excessively high value causes RFI from the switching too far from the zero crossing and can contribute to having some DC content in the output (important if the load has a transformer). The latter effect is due to asymmetrical triac trigger current in quadrant I vs. III. 

Usually you can directly read the typical power dissipation from the triac datasheet. In your case, the datasheet you linked above contains the following graph: 



Your conduction angle is 180° in this case. You should aim to keep the triac junction well below the absolute maximum value at maximum ambient temperature for decent reliability. Personally, I don't like to see the junction temperature much exceed about 100°C under any conditions. If it's losing gate control it's way, way above that (and any triacs exposed to that abuse should be replaced with new parts).