Yes it seems that there is shortened winding. Do a test, just simply connect to mains without connecting any load to it and see if heats same way, if YES, the trafo is short circuited and if the answer is NO then there is some thing wrong with the connected load, drawing over current and causing over heating. ( a very simple and quick test without ant any tools)the transformer is 100W, the preamp draws no more than 5w so is not overloaded.... but the transformer was very cheap, and so... its shorted as you mentioned.
There is explanation in text how this works in second picture is whole page of project, this is used for 220V to 110V, for other transformeless voltages you have other designs.
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