Not at all sure KK8
You would in fact have a double glazed area, the poly tunnel and the plastic covered thingy. But plastic does not hold heat like glass and without an actual heater I think that you could only hope for a degree or two maximum extra. I suppose you could nip out every night before you loose the heat of the day and wrap it in Bubble wrap or similar to help hold the heat
Sorry to be a pessermist, perhaps other Grapes have some other suggestions.
Can't spell today or it is too early, sorry!!!!!