The only reason I can think of as to why the transformer became very hot would be if the 5 Volt regulator (or micro) was consuming excessive current.
What current does the micro need? Did you measure the current?
I would use a 5 Volt regulator such as a 7805 (1 Amp max) or 78L05 (100 mA max) rather than a LM317 as you need less components.
I would also have used a 7815 (15 Volt 1 Amp max) and a 7915 (-15 Volt, 1 Amp max) for the +/- 15 Volt regulators. These are internally set to the voltage so you don't need resistors to set the voltage.
The LM317 is excellent for non standard voltages, but for the standard voltages, ie. 5, 6, 8, 9, 12, 15 & 24 Volt, the 78 or 79 series are better.
Note that there are also LM equivalents, eg. LM340T5 is equivalent to the 7805, etc.