An OT getting hot is normal. Try putting your hand on it after using your amp hard.
Simplified - the amp will try to push the same current into the increased load, which means it will have to provide an increased voltage. The OT gets punished. The output valves take a pasting.
Take a look at some valve charts, they and the data sheets will provide some optimum load value. This is the load of the primary. The actual resistance of the primary and secondary winding is very little. To obtain the correct load we multiply the speaker impedance by the turns ratio i.e. rearrange for resistance Vin/Vout = Iin/Iout = n where n is the turns ratio
Rprimary/Rsecondary = n^2 the transformer changes resistance by the square of the turns ratio.
A turns ratio of 31.6:1 would allow the output valves to see an 8ohm speaker as an 8kohm load,
- whereas the speaker sees the Thévenin output resistance of the output valves stepped down by an identical amount (the latter is an important distinction between valve and solid-state and goes some way to explain why valve amps are louder for the same power output)
If you were to double this example 8ohm speaker to 16ohm, you do not increase the load on the valves by 8ohm but by 8kohm!
And which is why small changes in speaker load have a big affect on the valve amp.
There's two kinds of people, those that hear the music and those that don't.