The paper describes a novel smart rotor support damper with variable stiffness made with a new multifunctional material - the shape memory alloy metal rubber (SMA-MR). SMA-MR gives high load bearing capability (yield limit up to 100 MPa and stiffness exceeding 1e8 N/m), high damping (loss factor between 0.15 and 0.3) and variable stiffness (variation of 2.6 times between martensite and austenite phases). The SMA-MR has been used to replace a squeeze film damper and combined with an elastic support. The mechanical performance of the smart support damper has been investigated at room and high temperatures on a rotor test rig. The vibration tuning capabilities of the SMA-MR damper have been evaluated through FEM simulations and experimental tests. The study shows the feasibility of using the SMA-MR material for potential applications of active vibration control at different temperatures in rotordynamics systems.