The calculated distance (air line) between Heilbad Heiligenstadt and Karlsruhe is approximately 181 miles respectively 291 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Heilbad Heiligenstadt and Karlsruhe has been calculated here.
Air line (approximately)
291 kilometers
157 nautical miles