Junction Temperature from Power and Thermal Resistance

Heat flow obeys a law with the same shape as Ohm's. Temperature difference plays the role of voltage, power in watts plays the role of current, and thermal resistance in kelvins per watt plays the role of ohms. So the silicon sits above the surrounding air by exactly $P R_{\theta JA}$, and the whole of thermal design is the business of getting that resistance down or that power down, because the ambient is rarely yours to choose.

The junction-to-ambient resistance is a chain of series terms, and knowing which one you can move matters. Junction-to-case, $R_{\theta JC}$, lives inside the package and is fixed by the part you bought — no cooler improves it. Case-to-sink depends on the thermal interface material, its thickness and the mounting pressure, and it is where a badly applied paste or a missing pad shows up. Sink-to-ambient is the term a bigger heat sink, more fins or a faster fan actually changes. If the junction-to-case figure alone already exceeds the budget, no cooling solution on the market will rescue the design, and the power has to come down instead.

Two numbers are routinely misread. TDP is not power draw: thermal design power is a target the manufacturer sets for the cooling solution, representing a sustained realistic heavy load, and a real part draws less at idle and can draw considerably more during a boost window. Sizing a heat sink to TDP and then measuring a higher junction temperature under a burst is not an arithmetic mistake. And "ambient" means the air actually entering the heat sink, not the room — inside a case that air can be 10 to 15 degrees warmer, and the error goes into the answer one-for-one.

The loop that makes this dangerous rather than merely inconvenient is leakage. Leakage current rises roughly exponentially with temperature, so a hotter die leaks more, which dissipates more, which makes it hotter. Below some cooling threshold the loop converges and the part settles at a stable temperature; above it, the loop diverges and the part destroys itself. This is why processors throttle so decisively, and why thermal design is done at the worst-case ambient with the worst-case silicon rather than at the typical numbers — the failure mode is not gradual.