Transformer impedance listed on the nameplate is the series impedance.
The impedance is a combination of Copper losses (I sqd R), eddy current losses, hysteresis losses, and leakage flux.
The percent impedance given is the magnitude of the combination of vector quantities, and is associated with the base rating of the transformer.
According to IEEE Std C57.12.01, Table 12 the allowable temperature rise of external parts, over ambient would be 65 deg C, regardless of internal temp ratings. So, with a 40 deg C ambient, the external temp should not be over 105 deg C. Keep in mind that is 221 deg F, and water boils at 100 deg C or 212 deg F under standard conditions at sea level (at one atmosphere of pressure).
For a std general purpose dry type 75KVA the 7.5% does seem high. I might expect something between 1.5% and 2.6%. 7.5% is high for any type that size, but it is what it is, just means it's poorly designed
If it is also making a lot of noise, then you could be exceeding the allowable dbA level, and is probably due to winding vibration. Heat could also be from non-linear loads if you have them.
Sounds like you just have a cheaply made transformer.
"Just because you're paranoid, doesn't mean they're not out to get you"