buildind a a auto switch to hold woud be easier, and run around $150.
Used temp controller $40 each
Snap Disc temp switch $15 (to maintain 150F)
One shot timer $50
Power relay $20
Thermocouple $10
Other $15
when the temp controller hist set point, it fires the one shot timer, which then puts control to the snap disc.
Snap disc turns on when the temp drops to 120F and off when the temp hits 140F (or any range with a 20F spread)
you would plug the cookshack into the, and this into the wall.
Once your food got the set point, the snasp disc would be controlling the power to the cookshack, and turning it off when ever it got over 140F.
you would have to stick a probe for the food and the snap disc down the vent hole.