You will probably electrocute yourself. You need to find bulbs and fixtures rated for outdoor use. In your attempts to keep your plants dry, you may make them even wetter -- they will respirate inside your closed mini-greenhouse and turn it into a soggy rainforest. Think about ventilation and a fan to keep the air moving.
People I know using those little greenhouses are putting 4 foot bulbs vertically in the corners. I don't know anyone who has used them outside. They are popular as greenhouses for indoor orchid collections (plants that like humidity).
To answer the rest of your question, T5's are more efficient than T8's so put out less heat than T8's.
This is the one I'm using.
https://www.amazon.com/dp/B00AKKUPSM/
