A fuel cell arrangement which comprises a fuel cell having a first inlet for a fuel and a second inlet for an oxidizing agent, and comprises a vortex tube having an inlet, a first outlet for heated gas and a second outlet for cooled gas. Here, the first outlet of the vortex tube is fluidically connected to the first inlet or the second inlet of the fuel cell. A fuel cell system may have such a fuel cell arrangement, and a vehicle may have such a fuel cell arrangement or fuel cell system.