The fact that higher harmonic content in the current causes higher eddy current loss in winding conductors and structural parts linked by the transformer leakage flux field and, consequently, higher operating temperatures. This is why the original install is running hot.
However, the answer is not to simply oversize as there is a negative effect in oversizing due to a lower ohmic resistance on the load harmonics that can cause the neutral line current to actually increase. The same effect is present when you use too high of a k-factor rating because with typical k-factor transformers reactance goes down when k-factor goes up.
At or near transformer full load is best and is where a k-rating may be necessary to prevent overheating since transformer losses vary with the square of current, therefore the losses for an over sized transformer with reduced loading has more negative impact, and also since transformers are most efficient around the 70-80% of their capacity. At full load is also where the transformer reactance will have the most effect in reducing the harmonics.
There are multiple transformers used for harmonics - K-factor, isolation, delta-wye isolation, phase shifting, auto, ferroresonant, and zig-zag. Each does something a little different.
In the end, the proper determination for the transformer should be done in accordance with IEEE C57.110.