Generally speaking a close approximation of the power dissipation in a triac is the average forward current times the "ON" forward voltage. Typically this voltage is less than 2 volts. For example the typical forward voltage drop in an 2N5445 is 1.7 volts in the "ON" state. This is good if you are using 50 or 60 hertz but may be much more if you are using a much higher frequency because of the turn on transition time. As Steve says the gate adds a little bit more.
When you say DC instead of AC what do you have in mind?