Yes. I would be worried about heat as well as UV rays (As the others here from Australia know, we have heaps of both). The seal around the edge between the two layers of glass that make up the LCD is very fragile. When the LCD is heated the liquid crystal chemical between expands which can damage this seal. If the seal is damaged the liquid crystal is slowly lost and the display ceases to function(usually starting with a small area and spreading from there. This damage can occur *SOME* LCDs.
Many are available in Extended Temperature Range versions. ETR versions can take a higher temp without damage and have slightly different electrical characteristics (often require a negative bias voltage. This allows for a temperature compensated LCD contrast).
Anyway to get to the point. I wouldnt worry about it for a character LCD. Even if the UV and heat kills it after a couple of years, it's cheap enough to replace. However, If I had a $600 TFT I would be a litte more carefull. You could try one of those little solar powered fans that such the heat out of your car when it's parked in the sun (I dont know how well they work. I've never tried one).