We introduce a superconducting transconductance amplifier based on the thermal modulation of a superconductor-insulator-normal metal-insulator-superconductor (SINIS) configuration. The device consists of a normal metal island interfaced with two superconducting leads via tunnel barriers, forming a voltage-biased symmetric SINIS setup. An additional normal metal-insulator-superconductor (NIS) junction connects the island to a third superconducting lead, which serves as an input. When the input voltage surpasses the superconducting gap, the resulting injection of quasiparticles increases the electronic temperature of the island, thereby modulating the SINIS current. We perform numerical analyses of the device performance, influenced by input voltage, frequency, and bath temperature. At bath temperatures below , the device shows a transconductance greater than and a current gain greater than . Both gain and transconductance maintain their levels up to , but decrease at higher frequencies, with a cutoff around , an input-referred voltage noise of 7.5 , and an average power dissipation of approximately 5 nW. Our simulations reveal a fully voltage-controlled, three-terminal, superconducting amplifier characterized by high transconductance and gain, enabled by thermally mediated signal transduction. This architectural design presents a promising avenue for cryogenic amplification with reduced power dissipation and compatibility with current superconducting electronic systems.