Installing an electric toe kick heater "old work"-style
I suggest you install a junction box in the wall, and hardwire the appropriate gauge wire through the cabinet bottom, to your heater. 

The cabinet is made of wood, you can drill through obstacles to thread your wires.

You need to leave enough slack so you can easily pull the heater for maintenance and cleaning. I recommend a metal flex pigtail with individual wires. On a GFCI circuit.

Which amperage is your heater? Internal thermostat or wall mounted switch/thermostat?