The 25VAC transformer produces a peak voltage of 35.4V which is reduced to 33.4V by the rectifier bridge. Then try to turn the voltage down to 1.2V at 1.5A then the regulator will heat with (33.4V - 1.2V) x 1.5A= 48.3W which is way too much heat for it. Luckily it has thermal protection built-in so it shuts down when it gets too hot. If the output is set to 5V and loaded with only 1A then the LM317 will heat with (33.4V - 5V) x 1A= 28.4W which will also cause it to shut down even if it has a HUGE heatsink.
Therefore reduce the voltage from the transformer.