Higher compression equals heat?

Referring to (Pressure Volume Cycle). Do higher compression engines run cooler than lower compression engines? Higher compression should have have higher pressure at TDC, thus more heat but in this session it's stating the opposite. Please explain. Thank you!

https://www.hpacademy.com/dashboard/courses/efi-tuning-fundamentals/engine-principles-pressure-volume-cycle

The temperature of compression is higher, however as the engine is more efficient with a greater power stroke expansion ratio, less total fuel/air is required to generate the same power, hence less total heat rejected to coolant/oil and exhaust.