A triac drops about 1.1V, so at 3kW (12.5A), that's going to be about 14W from the triac.
Phase control of a 3kW load will generate quite a bit of noise on the mains too, even allowing for RF suppression. Power control of heating loads is normally done by using zero crossing switching (e.g. on for 3 cycles, off for
3 cycles), as it avoids switching the mains other than at the zero crossing points, and so generates no noise.When I've designed phase control circuits for high power, I have used MOSFETs instead, which will have half the power dissipation of a triac (and that's only because it's AC, otherwise it would be much less). You can also do some more interesting things, such as switching on and off more than once per half-cycle, e.g. just switching off at the cycle peaks. However, you need different driving circuitry, and you need two MOSFETs (for AC).