Found a leopard gecko

[Vesper]

So, I'm at work at the moment and I was walking about and I found this leopard gecko (I'm pretty sure it's a leopard gecko, from what I've seen online). How it got all the way out here is questionable...maybe it hitched a ride in someone's vehicle and got out?
Anyway...he's really cold right now, it's in the high 50's. He's been moving really slow. I cleaned out one of my food containers and made holes in it before sticking him in there and I put him under the desk with a little space heater on in his direction (although some feet away from him as well). I might have a heating pad in the car, and was thinking if I could find a box I could put the pad on one end, keep him in the container on the other and maybe that'll warm up a space for him. Do you think that'll be enough for him until I get home? D':

He looks all right otherwise, not too thin, so I don't think he's been wandering around for long. I don't know how it could survive the temperatures if he was...

Any at rate, I know nothing about leopard geckos, or geckos in general. I'm going to ask a couple of the guys here to see if maybe...they had an escapee at home, but if none of them do...then I'm taking him home. I've got an extra plastic tub. Would he be ok in that? And then food...I've read mixed things about what to feed them. Some say only crickets, some say mostly mealworms and a few crickets...some say mealworms are worthless in nutritional value. Some say mealworms for the most part, and then add variety with crickets, roaches and other worms..

Any other info/tips is appreciated too.