In plating operations what you are paid for is a specified amount of material thickness properly applied. Too little means a poor quality job and a lost customer any extra comes from your pocket.
The plating rate for a particular process is controlled by current, time, and temperature. Unless you artificially control temperature the bath is always changing with the ambient which can vary quite a lot over the plating time for a run.

Power dissipation simply put is power in - power consumed by the load. In this circuit the dc input is fixed at 20 volts so input power is 20 X 3 = 60 watts. Tank voltage while unknown will be less probably about 5 volts or so to leave room for higher currents and good compliance so about 15 watts into the tank leaving 45 watts to dissipate in the LM338, TIP3055 and the resistor R12.
As Steve mentioned a switching regulator with feedback would reduce the input voltage to perhaps 10 volts for a bath voltage of 5 volts.
the input voltage would be approximately V bath + V constant current source minimum ( the minimum drop voltage across the constant current sink varies with the current setting) plus a couple of volts for compliance . The feed back would cause the switcher to track required input voltage changes caused by changes in current setting.
Older supplies used control windings on the transformer to control the dc input magnetically with a buck winding. No where near as efficient as a switcher at 90% or better efficiency but in the 60 to 70% range as compared to 20 - 30% for a simple supply
such as yours

Kai is correct that op amp should be configured as a unity gain voltage follower.

R 12 is the element that controls the current. By changing the value of this resistor you change the range of the CC sink and the ease of setting your desired current. Other design criteria are affected by the chosen value as well.
It is normally selected to make full use of the pots range to achieve full current range.
Terry