Can someone help me design a circuit that will open when power is applied and close after power is removed?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A thermostat-controlled solenoid.

What you are describing in your question could be solved with the simple circit of Figure 1.

How it works:


When the thermostat threshold is exceeded the T'STAT contact closes and 6 V is applied to the solenoid. Your door should open.
When the temperature drops below the threshold the T'STAT contact opens again, power is removed from the solenoid and your door should close.


This seems so trivial that I suspect there is some complication that hasn't been explained in your question. If you clarify your question we can address the problem more appropriately.