You probably burn less than 1/2 gal per hr idling the engine w/AC on. If you have remote start, go to bed and use the remote start to start it up. If you run it for 6 hrs of the night, that's probably 2 gallons of gas, depending on engine size, etc. 2 gallons of gas right now costs approx $6...
why not use a regular LED lantern for the 30 mins needed to get ready for bed? If that's all it's used for, one set of batteries should last for 5 nights if only used for 30 mins each night.