A thermal frame of an imprinting apparatus has an motor and a cooling element. A metrology frame of the imprinting apparatus is coupled to an output end of the motor and receives an imprinting mold. Thermal isolation is provided between the motor and the metrology frame. Thermal sensors are disposed at locations of the frames. A digital controller applies a control signal for controlling a driving signal of the cooling element to maintain a thermal balance, such as thermal equilibrium, of heat flow between the frames. The digital controller uses output of the thermal sensors to identify transfer functions of heat flow used to calculate the control signal. The feedforward design avoids the very low control bandwidth that limits the performance of typical feedback designs.