No problems to date and have many of the first sets etc.
However, 20+ years ago our prior home had a sun room of sorts. There were several ledges etc and I thought some of my painted collection would look good setting out. So a couple hundred or so were set in place, looked great as the SUN rose behind them etc. Then we moved, and I took my little guys down, and bingo, they started to fall apart at the touch. Those the did not break had their paint falling off....so it seems I leaned that sun, heat, and being stupid was a hazard to my guys. Since we moved and I have a basement with my 'room' no problems, I keep them out of direct sun and the lower level is always cooler then the rest of the house. So IMO it seems sun and heat are the enemies as opposed to the plastic itself.