Contactors ARE mechanical relays. And in this (and almost every other controller) design the element isolation contactors are not being driven by the PLC's PID. The PID controls switching of the SSRs, which are what actually modulate power to the elements. The contactors/relays are used to enable/disable power to the elements by providing galvanic isolation.Are the relays actually contactors and not mechanical relays? The later can't handle the fast switching of a digital controller. Not sure if they aren't heating at all or just getting warm.
Also, the OP has diagnosed the issue as faulty structure wiring in the circuit that was supposed to provide power to the controller. Essentially the controller wasn't completely "plugged in."
Brew on