I'd certainly try it out for a day or two a week, backpack / jersey pockets for stuff.. easier if you have a locker or showers at your work. Hopefully you wouldn't arrive too sweaty after 3 miles which should take you about ~15 minutesish.

Win-win though, exercise and if you get in to it less fuel costs. Could easily clock up 30 miles a week and extend your route on nice days.. no brainer!

The best thing you can do to avoid getting sweaty is use either a basket or pannier bags to carry your stuff.