AC superconducting coils have losses which warm up the coil and so limit the performance. Good thermal contact between the coil and the cooling agent is important. Cooling of the coils by heat conduction through solid conductive material is no option since very large eddy-current heating would be generated in the thermal bridge. Previously we analyzed cooling by a cryocooler where the cooling power was distributed by a flow of cold gas over the coils, driven by a fan. Presently we investigate the possibility of cooling the coils with a cryofluid, such as hydrogen or nitrogen, obtained from a reservoir and flowing through capillaries in close thermal contact with the coils. In our contribution the technique will be introduced. We report on recent experiments where the AC losses are simulated by electrically heating capillaries under conditions which are comparable to the conditions in the application. In particular the behavior near the maximum cooling power will be described.