Well, maybe in some rare cases but this one can be cooled by mostly anything. The 3D v-cache feature allows it to run cooler with low latency.

No. Where did you hear that? Heat is generated from Watts. The power draw of the 7800X3D is less than the 13700K.

7800X3D 8 cores 16 threads TDP 120W Actual power draw ~86W 13700K 16 cores 24 threads TDP 125W Max Boost 253W avg power draw 133W peak draw 250W

Tom’s Hardware 7800X3D avg max power draw

Intel i7-13700K power draw

The 7800X3D is waaaaaay more efficient and therefore cooler than the 13700K