A few weeks ago I left out a big cardboard box camera with a piece of color photo paper in it.... I was trying to make a "retina print". It was out for around 8 or 9 hours and I didn't mean to but I got a sun streak on the paper. I agree with NT, over the course of a week or so you could probably get multiple sun trails.... the paper I was using is slow slow slow... it took three days to reach max dark grey sitting on my desk!
But I would worry very much about starting a fire and it might not be good enough to see that a fire doesn't start in a day or two... like leaving a magnifying glass in your window aimed at a piece of paper and hoping that it doesn't catch your house on fire... you might not want to feel safe just because a fire didn't start in the first day or two!
I agree with John that a pinhole over the lens is a good idea and it will not affect your coverage. The result will be like a "sharper pinhole" and you won't have to worry about burning down your house!