Can I keep a camera in my car's glovebox?

I have decided I'm going to buy a Nikon D3100(digital SLR)… But to get my money's worth out of such a huge investment would require me to take advantage of every opportunity to take photos. This means leaving it in the car when I'm not at my place or a hotel. Would this destroy the camera?

You must have quite a large glove box! I'm not sure where you are, but my car here in the UK (Rover 25) would certainly not hold an SLR and lens in a case. If however your car is large enough to hold it on the glove box then I don't see any reason why not, providing you have it in a nice strong case that will prevent it from damage should it be thrown around within the compartment.
I think that perhaps a more suitable alternative would be to keep the camera and lens(es) in a more sturdy camera bag and keep it in the boot of the car, a few blankets thrown on top to keep it more held down and protect it from damage. Don't forget that if a thief was to break into your car, they are going to check the glove box for items such as a satnav. A DSLR is a nice find for a thief, but in the boot under a blanket? More difficult to locate.
I always carry a camera in my glove box, a little Olympus MJU II in a case. It is nice to have a camera in the car at all times because I can think of dozens of occasions when it has been useful for taking shots on unexpected occasions. Perhaps consider this. Buy your DSLR but keep it at home. Use it when you KNOW you are going to somewhere where you can use it. Buy a small compact film or digital camera to keep in your glove box, for those occasions when a DSLR is not handy, or you don't have it on you.
They say the 'best' camera is the one you have on you at the time, this is very true!

A car isn't going to do it any good, certainly not if you live somewhere warm

Keep there? Yes. Destroy? No.
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