I don't think anyone would rent you a tent for Burning Man, sadly, even if you managed to find someone who rents tents. Having borrowed a friend's tent last year I can tell you that that tent will never be the same. I cleaned it three times and there's still playa dust in all the seams. Thankfully he's joining me at the burn this year and using the same tent, so no real damage done.
That being said, I imagine it would take you approximately zero minutes to find someone who would love a gift like a tent at the end of the week, provided it isn't total rubbish.
Coleman Sundome's are good, cheap options. The 3 man version (9'x7' or 2.7mx2.1m) run about 50 USD on Amazon. They unfortunately have top vents you'll want to cover somehow (numerous threads here on securing tents to minimize dust issues) but other than that they're very well made and will survive the burn and make a fantastic gift or donation (Good Will, etc).