My mechanic has been a mechanic for both IMSA and World Cup Challenge teams, and he went over some of the changes that are seen from road-going versions of what he normally works on (Porsches). Things like heat exchangers have better conductive materials, coolant lines will make multiple passes instead of a single pass, and there are more lines (to increase the surface area of the line), packed in more densely. Coolants used are optimized for a specific temperature range, since they don't have to deal with global conditions of a road car all over the world.

More complex machining for passive cooling (heatsinks) of transaxles, higher airflow towards brake rotors (with specific shield designs, part of which are backed out to catch more air).

The biggest change? Fewer fans, and only as many as required, as they inhibit airflow. Convection does the job well enough as race cars aren't sitting in traffic in hot climates, and aren't sitting around long enough to heat soak from being stationary (but are why the pit crews have blowers). As much aero design goes into routing air for maximizing cooling as there is for creating downforce.

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Formula 1 and WEC (which are more like ground aircraft than anything resembling a road car) are a different story though. Things like the intercoolers for turbochargers are absurdly complex. You're talking four passes through the intercooler, and lines that are basically long surgical needles, with ~13000 packed into each intercooler. All hand built, all very expensive.