My arduino gets hot when us a 12 volt adapter

It's not to difficult to make a buck or boost switcher to handle whatever input voltage you want to deal with. The other option I suggested above is to get a car cigarette lighter that gives you the output voltage you need. Some are simply voltage regulators, but some are buck switchers. If you live in an area that has "Thrift" or second stores you can usually pick these up for a couple of dollars. Then you can take the little board out of the case. Just 2¢ here.