I have replaced the temporary clamps that were connecting the RC heater to its power supply with a new permanent connection.
In the IY1 rack, I connected the control signal of the RC PID temperature servo - C1:PSL-FSS_TIDALSET - to the input of the RC heater's power supply.
The signal comes from a DAC in the same rack, through a pair of wires connected to the J9-4116*3-P3 cross-connector (FLKM). I joined the pair to the wires of the BNC cable coming from the power supply, by twisting and screwing them into two available clamps of the breakout FKLM in the IY1 rack - the same connected to the ribbon cable from RC Tmeperature box.
Instead of opening the BNC cable coming from the power supply, I thought it was a cleaner and more robust solution to use a BNC-to-crocodile clamp from which I had cut the clamps off.
During the transition process, I connected the power supply BNC input to a a voltage source that I set at the same voltage of the control signal before I disconnected it (~1.145V).
I monitored the temperature signals and it looked like the RC Temperature wasn't significantly affected by the operation.