 First-order thermal isolation

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.