We investigate bias-point engineering of a quantum thermal transistor using a minimal set of thermal baths. A hot bath at temperature $T_1$ injects heat into a metallic conduction bar coupled at its far end to a qubit, while both the bar and the qubit exchange energy with an environment at temperature $T_e<T_1$. From a microscopic transport description of the bar, we derive a compact steady-state energy-balance model by identifying temperatures as node potentials and heat flows as branch currents. The resulting formulation gives closed-form expressions for the steady-state heat current and temperature drops across the bar-qubit network and determines the conditions for proper thermal biasing. We further show that conduction bars and baths can be arranged to function as tunable thermal potential dividers, known as quantum thermal links, enabling transistorlike control of the heat current delivered to the qubit terminal. Linearization about the bias point yields small-signal thermal analogs of Kirchhoff's current and voltage laws. These results provide a first step toward a circuit-based framework for the small-signal analysis and design of thermotronic devices.

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• Heat transfer
• Quantum thermodynamics
• Thermal properties
• Transistors