I don't think it's crazy, but I think you'll be all right, in terms of the sun and its heat.
What you might want to consider, however, is some protective film, just so it doesn't get scratched. When I took delivery of my C 400 GT a couple of months ago, I bought some protective film from Wunderlich:
Check out the deal on Instrument Protection Film at wunderlichamerica.com
www.wunderlichamerica.com
This package included two films: a clear (i.e., just protective) and a matte (i.e., protective and anti-glare). I put the latter on, and it's been fine. Wunderlich doesn't seem to list much, if anything, for the CE 04, though, and I don't know whether your scoot and mine have the same size TFT screens (although Wunderlich might know). I did a quick search -- googling
bmw ce-04 screen protector -- and found some sites that offer protective films, so you might want to check them out.