Minimizing the Vdifference (Vinput - Voutput) to keep the temperature of a regulated power supply low, requires a transformer's secondary voltage, that matches your application. The secondary's voltage has to be as low as possible to generate as low heat as possible), but high enough, to always and in all situations keep enough headroom available for the regulation. It should be noted, that the charge stored in the capacitors occurs in the form of ripple.
Ripple increases with increasing load, or in other words: the more current your device consumes, the more does it discharge the smoothing capacitors (time of discharge), resulting in increased ripple.
Here is an approximate formula for determining the amount of ripple on an unregulated power supply:
Vrip = ILoad * 0.007 / C
Vrip = Voltage ripple value (V) ILoad = Current of the load (A) C = Capacitance of Capacitor (F)
ILoad = 0.1A C = 1000uF or 0.001F
We can calculate the ripple as following:
(0.1 * 0.007) / 0.001 = 0.7V
Finally the best possibility to measure the ripple in your power supply is to use an oscilloscope.