Rhome was hired in 1935 as the athletic director at Texas Wesleyan College—now known as Texas Wesleyan University in Fort Worth, Texas and was charged with coaching football, basketball, and track. He led his Texas Wesleyan Rams football teams to records of 8–2–1 in 1935 and 3–6–1 in 1936. Rhome left Texas Wesleyan in 1937 to become head basketball coach at Sunset High School in Dallas. He was succeeded as Texas Wesleyan's head coach in football, basketball, and track by Gus Miller. Rhome coached the 1944 Hondo Army Air Field Navigators football team to a record of 7–1.
