First-order thermal isolation ($C\dot{\delta T_s}+G\delta T_s=G\delta T_b+\delta P$)

A lumped sample of heat capacity $C$ coupled by thermal conductance $G$ to a bath has the displayed linearized energy balance. For constant internal power, the bath-to-sample temperature response is $1/(1+i\omega C/G)$. Insulation and heat capacity suppress rapid bath fluctuations but have unity static bath-to-sample gain. A steady power change shifts the sample by $\delta P/G$, so improved isolation increases self-heating sensitivity and equilibration time. The lumped approximation requires internal equilibration faster than the variations being modeled.

A first-order lumped thermal system relaxes exponentially with time constant $C/G$ after a small bath-temperature or heating change. More complex systems have multiple thermal modes and need not have a single relaxation time.