He has 48v CENTER TAP , and he says he has a "dual polarity" power supply.
I assume from that he has +/- around 24 v , somewhat like this design:
There's only one forward voltage drop as only one diode works on each side so let's just neglect it in this situation.
Also going to assume the capacitor is big enough so that we won't have much ripple (assume the voltage regulator has 24v at the input).
Then at 12v 500mA of current, your linear regulator will dissipate as heat the following
(Input Voltage - Output Voltage ) x Current
and that's (24-12 )x0.5 = 6 watts.
At 0.36A , you have about 2.1 watts. A small heatsink should be enough to dissipate the heat away from the regulator.... not sure though, it's not clear exactly what the input voltage each regulator receives.