  We propose a thermal transistor based on a three-terminal
normal-superconductor (NS) junction with superconductor terminal acting as the
base. The emergence of heat amplification is due to the negative differential
thermal conductance (NDTC) effect for the NS diode in which the normal side
maintains a higher temperature. The temperature dependent superconducting
energy gap is responsible for the NDTC. By controlling quantum dot levels and
their coupling strengths to the terminals, a huge heat amplification factor can
be achieved. The setup offers an alternative tuning scheme of heat
amplification factor and may find use in cryogenic applications.
