I sometimes have only one shirt. Typically on trips where the weather is expected to be very moderate (35-55F) or when I am trying to go SUL.
I have never had a problem with it being too sweaty before going to bed because it dries very quickly (powerdry or coolmax featherweight). I have gotten under the covers when the shirt was soaks by rain, but found that it dried pretty quickly once I was out of the rain and my body could heat it up.
Most of the time though, I bring a second shirt. There are two reasons. In warmer weather it's because my daytime shirt (supplex) starts to stink and isn't the most comfortable thing to sleep in. So I want something less smelly and softer. In colder weather I was more insulation fo my arms than my daytime shirt provides. I have been known to use my "sleeping shirt" during a hike when the weather turned out to be surprisingly cold… so I really treat it more like a light insulation layer than a sleeping shirt.
–mark