The rain forests themselves will be quite a bit cooler -- they tend to average 80F/27C, with temperatures rarely much higher than 92F/33C. I think it's a side effect of the constant rain.
I'm not sure about your non-rain forests. It's possible they are seasonally operating at a loss -- storing sugars during the cool seasons and burning them during the hot seasons.
As I've said, there are big areas of rain-florest in Brazil that rarely see less than 38°C during the day. There are also big areas of savanna that stay around that temperature for half a year (the half that rains). The fact that there are also cooler areas does nothing to explain how plants survive on those both.
I do think it's quite likely that plants keep leaves bellow the environment temperature, I'd just like somebody that knows it to confirm it or not.
I'm not sure about your non-rain forests. It's possible they are seasonally operating at a loss -- storing sugars during the cool seasons and burning them during the hot seasons.