Hi - I don't know what type of temp gauge your Bugeye has but most MG Midgets (like my 76 Midget) use a metal bulb and metal line (filled with ether). The temp gauge isn't like the normal electrical type and doesn't require electricity. They can be repaired. Here is an article on how to repair one.
Also, there are instrument and gauge repair shops listed in Hemmings Motor News. Check Hemmings Motor News on-line or buy a copy at your local bookstore.
Hope this info helps.