First thing -- assuming your input voltage is 12V, are you using a 220V to 12V transformer as a step-up transformer?
If so, you have 2 problems. The first is that there is some inefficiencies, so a 220 to 12V transformer used the other way will produce only (say) 200V -- however you'll notice this mostly under load. The second is that the peak voltage of 12V AC is almost 17 volts, so if you are switching a 12V source to a 12V winding, you're effectively providing (probably) a lower voltage.
The latter effect would give to approximately 155V. The former effect may be the cause of the voltage falling further under load.
The heating may be caused by your load. What is the transformer rated at, and what is your load? (I suspect you're using a simple square wave too, and that certainly won't help).