Substrate-attached and freestanding single crystalline Fe70Pd30 ferromagnetic shape memory alloy membranes, which were synthesized by molecular beam epitaxy on MgO (001) and later released from their substrates, are characterized with respect to their structural, thermal and magnetic properties. Residing in the two-phase region of austenite and the correct martensite phase with face centered tetragonal (fct) structure at room temperature, they reveal martensite transition with little hysteresis at 326 K and 320 K, respectively. Comparing substrate-attached with freestanding films, which show fundamentally different magnetic fingerprints, it is proposed that domain structure is capable of posing a bias on the austenite ? fct-martensite phase transition by favoring martensite variants with their easy axis aligned along the field just as the substrate constitutes a mechanical constraint on the transition. If confirmed, this would suggest thermo-magnetic actuation as an alternative where only moderate magnetic fields are feasible, but moderate temperature changes are possible.