Just a wild guess ... but think for a moment ... how does a dimmer work? Usually by letting only part of the sine wave through. Where does the rest go? Back into the grid.

Would the unused part of the wave cause additional heating, or other problems, inside the transformer?

IMO, dimmers and transformers are a problem looking for a place to happen.
If you're controlling a resistance type load - incandescent lights and heaters - then perhaps an autotransformer is what you really want.
If you're controlling a motor, then a VFD is called for.

If it's a DC load, then control it AFTER the DC is created. Just my thoughts.