A heat engine includes a first rotatable pulley and a second rotatable pulley spaced from the first rotatable pulley. A shape memory alloy (SMA) element is disposed about respective portions of the pulleys at an SMA pulley ratio. The SMA element includes first spring coil and a first fiber core within the first spring coil. A timing cable is disposed about disposed about respective portions of the pulleys at a timing pulley ratio, which is different than the SMA pulley ratio. The SMA element converts a thermal energy gradient between the hot region and the cold region into mechanical energy.