Ok, so the more amps you put out through a power supply and the lower the voltage, to more heat produced, correct?
Right
So if I run an LM350 and supply it with 2 amps, I need to keep the voltage from the transformer as close to my operating ranges as I can? If I want to run between 1.25 and 18 Vout, then I need no more than a, roughly, 19.5V output transformer? Anything more will result in more heat?
Now you got it. Right again.
Like Kiss said, it's a little more complicated about the transformer. Transformers are speced in RMS but once thru the bridge it will charge the caps to peak voltage which is 1.414 times higher than RMS. I think the last one we used was a 16 volt one which would charge the caps to 22.6 volts. We will loose about 1.2 volts thru the bridge so 21 volts into the regulator. But wait, there's more!
The caps only get charged when the sine wave from the transformer is higher than the voltage on the caps. So in between peaks the voltage will sag. This is called ripple. The higher the current draw for a given capacitor the higher the ripple. This is also why the transformer needs a higher current rating than the load. And finally the regulator needs some voltage higher than it's output to regulate. This is often in the spec sheets as drop out voltage and also depends on how much current you draw. The advantage of the switch that Kiss is talking about is that the output of the transformer can be cut in half. This is nice for power, but you would have to stop and switch then readjust the voltage.