Burghaun is a municipality in the district of Fulda in the state of Hessen in Germany. Burghaun itself is a small town with about 3,800 residents. …Burghaun is a municipality in the district of Fulda in the state of Hessen in Germany. Burghaun itself is a small town with about 3,800 residents. Following the administrative reorganization of Germany in 1972 when smaller communities were grouped together, Burghaun took in the nearby villages of Großenmoor, Gruben, Hechelmannskirchen, Hünhan, Langenschwarz, Rothenkirchen, Schlotzau and Steinbach.