James C. Dempsey Jr.James Carlyle Dempsey Jr., 71, a building contractor, died early today at Wilson Memorial Hospital.The Rev. Philip Byrum will conduct the funeral Thursday at 11 a.m. at St. Timothy’s Episcopal Church.Surviving are his wife, Katharine Fleming Dempsey; a daughter, Katharine Rogers of Charlotte; three sons, James C. Dempsey III of Raleigh and Charles C. Dempsey and Julian L. Dempsey, both of Wilson; a sister, Elizabeth Leedy of Orlando, Fla.; a brother, Don G. Dempsey of Greenville and five grandchildren.The family will be at 1700 W. Nash St.Arrangements are being made by Thomas-Yelverton Funeral Service.