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