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A heat sink receives thermal energy from a component and provides a path for exporting it to a surrounding fluid or another reservoir. A metal block can spread a localized heat load by thermal conduction; fins enlarge the surface available for convection and thermal radiation. The entire path also includes the thermal resistance of the contact between component and heat sink.

For a simplified steady linear model, a component dissipating power $P$ sits above the ambient temperature by $\Delta T=P{R}_{\mathrm{th}}$, with total thermal resistance $R_{\mathrm{th}}$. Increasing a block's heat capacity can slow its transient warming but does not by itself lower this final temperature rise. This distinction can be tested with a fixed-power heating step: the early slope probes storage, while the long-time rise probes transport. A heat sink therefore needs an effective route to the environment as well as material that conducts heat internally.

At fixed face temperatures, differentiation of the thermoelectric cooler energy balance givesThus current chosen for maximum cooling power is not automatically current for maximum coefficient of performance. Cooling exists only when $(\alpha T_c{)}^2>2RK\Delta T$, and then only between the two positive rootsAt equality the parabola merely touches $Q_c=0$. For the toy module the interval is approximately $0.767<I<10.433\mathrm{A}$, with $I_{\ast }=5.60\mathrm{A}$ and $Q_{c,\max }=23.36\mathrm{W}$. At $12\mathrm{A}$, the object is heated even in the nominal cooling polarity: $Q_c=-17.6\mathrm{W}$. This mathematical interval supplies no permission to exceed an actual device's current or temperature ratings.

The fixed-face constraint matters. With fixed $T_h$ but a freely cooling object, $T_c$ must be solved from its heat load and leaks rather than held at $280\mathrm{K}$ while claiming an arbitrary temperature drop. For zero load and optimal current, the same model givesHere $Z$ has units ${\mathrm{K}}^{-1}$ and is a module parameter. The toy model gives $Z=0.0020{\mathrm{K}}^{-1}$ and $T_{c,\min }\approx 241.62\mathrm{K}$ when $T_h=300\mathrm{K}$. This is an ideal zero-load limit with stipulated constant properties; cooling a real load requires $Q_c$ above zero and reduces the attainable drop. Contact thermal resistance, a warming heat sink, external leaks and temperature-dependent coefficients further change the result. Electrical control is convenient, but conservation of energy still requires a thermal path that removes the extracted heat plus the electrical input.