You can get buck regulators (not just the IC, a complete module with caps, etc.) off ebay for about $1. It will run much cooler and be far less messing about. Or get a cigarette socket phone charger for a few dollars, it will do the same thing in a neat package.
IMHO, unless you need low ripple or are pulling very low current, there are few situations where a linear reg would be better than a switcher. Cost used to be a factor but that is no longer the case.