There are a no of test available for gram positive and negative bacteria, according to your requirement and availability of laboratory you can choose e.g. Coagulase test
Look at the papers that contain the descriptions of new thermophilic bacterial species. See the attached file---"thermophiles.txt"---which contains all bacterial species from "A" to "T" described in the papers that contain "thermophilic" in the title (so, beware---not all the listed species will be thermophiles). For the links to the papers, see "Bacteria I. Names" . . .