Ciovati, G. Anderson, J.P. Balachandran, S. Cheng, G. Coriton, B.R.L. Daly, E.F. Dhakal, P. Gurevich, A.V. Harding, K.A. Holland, L.D. Marhauser, F. McLaughlin, K.R. Packard, D.A. Powers, T. Pudasaini, U. Rathke, J. Rimmer, R.A. Schultheiss, T. Vennekate, H. Vollmer, D.M. JACoW Publishing Geneva, Switzerland Recent progress in the development of high-quality Nb₃Sn film coatings along with the availability of cryocoolers with high cooling capacity at 4 K makes it feasible to operate SRF cavities cooled by thermal conduction at relevant accelerating gradients for use in accelerators. We have developed a prototype single-cell cavity to prove the feasibility of operation up to the accelerating gradient required for 1 MeV energy gain, cooled by conduction with cryocoolers. The cavity has a ~3 ¿m thick Nb₃Sn film on the inner surface, deposited on a ~4 mm thick bulk Nb substrate and a bulk ~7 mm thick Cu outer shell with three Cu attachment tabs. The cavity was tested up to a peak surface magnetic field of 53 mT in liquid He at 4.3 K. A horizontal test cryostat was designed and built to test the cavity cooled with three cryocoolers. The rf tests of the conduction-cooled cavity achieved a peak surface magnetic field of 50 mT and stable operation was possible with up to 18.5 W of rf heat load. The peak frequency shift due to microphonics was 23 Hz. These results represent the highest peak surface magnetic field achieved in a conduction-cooled SRF cavity to date