Welcome to the forum. I do not have experience w turtles but I.M.O all frogs benefit from some lighting. I have a daylight blue bulb for my gray tree frog which provides enough heat as well. Obviously they are different species, but I am sure someone on here specifically knows more about green tree frogs and can help you. If temperatures are cooler than recommended a lot of frogs tend to slow down and begin to go into a hibernation like phase. Mine did that for a few years. This is the first winter she has not due to the higher wattage bulb I have now that is keeping her tank at a good 75-78 degrees during the day.