Sorry, but you are almost certainly completely wrong:
1) The wires aren't bare, they are varnished, same as almost every small transformer out there.
2) It's unregulated, so the voltage will be
MUCH higher than expected without full load.
3) It's a small mains transformer it
WILL run very hot, this is perfectly normal - basically the transformer, the less efficient they are. Large transformers (power stations etc.) are pretty well the most efficient machines that are made.
4) If the wires had somehow rubbed through the varnish and were touching, that would cause a shorted turn - and you'd know it was getting
HOT then