Wiring Transition from Inside of wall to Outside of Wall for hard-wired appliance
It seems like the space under the cabinets is inaccessible and would be treated like the interior of a wall. 

In that case, you could merely cut a hole in the wall at the back bottom of the cabinet that will hold the heater and continue your cabling into the opening that will hold the heater. 

Once the cable is attached to the heater and the heater is pushed into the opening, the cable is protected.

Access to connections by removing a fixture is generally considered code compliant.