Thermoelectricity is a promising avenue for harvesting energy but large-scale applications are still hampered by the lack of highly efficient low-cost materials. Recently, Fe2YZ Heusler compounds were predicted theoretically to be interesting candidates with large thermoelectric power factor. Here, we show that under doping conditions compatible with thermoelectric applications, these materials are prone to an unexpected magnetic instability detrimental to their thermoelectric performance. We rationalize the physics at the origin of this instability, provide guidelines for avoiding it, and discuss its impact on the thermoelectric power factor. Doing so, we also point out the shortcomings of the rigid band approximation commonly used in high-throughput theoretical searches of new thermoelectrics.