Instead of burning the $10k, why not use a couple thousand and get something new with low payments until you save up some more and then pay it all off?
Don't get me wrong, I do similar and I got lucky when I found my Honda a couple years ago, 5 years old, 70k miles, V6 coupe for just under $10k but I had to look for several months and bought it from a slightly shady dealer, not a big name lot. Just went over 100k miles on it.
I really don't trust Hyundai in the used market but that's me.
You could find a nice Honda for about $15,000 used with lower miles, put 2,000 down, pay around $300 a month, keep using the money you were setting aside for the purchase, save up a few more months and then just pay it off. I understand it is more than you want to pay but in the long run you will get your money back out of it. Maybe in 2-3 years you trade that in, get $10,000 for that vehicle, get yourself a newer car. I'm just offering up another solution but I would not settle on a used car if it isn't what you want. It could cost you even more in the long run and I have had too much success with Hondas for anyone to tell me otherwise. Put gas in, change oil on time, change tires, do the maintenance as it is suggested, never an issue.
I also live in South Florida and while it is hot as the dickens down here, not exactly the horrendous weather you run into up North.