Heating a 2x2x5 container

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So im thinking about starting a grow up in my tree house..
was debating whether or not to post this in indoor or outdoor grow.. but im pretty much treating this like an indoor grow

once i have an actual plant in the pot i want to put it in like a 2x2x5 plastic box.. i guess, and put it in my tree house

im livin in seattle, wa.. so the weather is pretty shitty out here and to keep the temp in the high 70s i was thinking about throwing a heat lamp pretty much in the container to keep it a steady temp. along w/ all the other stuff i need in there (lights etc)

let me know what you think.