Was one of William Clark's brothers named Thomas W Clark?

No. Thomas W Clark was not William Clark's brother.

William Clark's brothers' names were: 1.) Gen. Jonathan Clark (b. Aug 1, 1750) married Sarah Hite. 2.) George Rogers Clark (b. Nov 19, 1752) revolutionary war hero and never married 3.) Capt. John Clark (b. Sept 15, 1757) 4.) Lieutenant Richard Clark (b. Sept 15, 1757) 5.) Capt. Edmund Clark (b. Sept 25, 1762)