Triac dimmer burned transformer as load
Do you remember when I told you about Quadrant IV on the triac? 

Remember when I said that if you don't put enough current into the gate (>100mA) the triac will trigger only on the (positive) half-cycles? 

That is equivalent to putting half-wave rectified DC through your transformer primary and "burning" is exactly what we would expect to happen. 

You need to either stop trying to trigger in Q-IV or to put enough current through the gate to trigger in any of the quadrants. 

And put a fuse in series with the transformer primary. It may not save the triac but it should save the transformer winding.