The calculated distance (air line) between Heilbad Heiligenstadt and Nürnberg is approximately 139 miles respectively 224 kilometers.
By car or train, the actual journey to Nürnberg is certainly longer, as only the direct route (as the crow flies) between Heilbad Heiligenstadt and Nürnberg has been calculated here.
Air line (approximately)
224 kilometers
121 nautical miles