Direct drive is thought to be (and I think proven as well although I can't bring any studies immediately to hand) more efficient in terms of converting power to tractive effort. Since you'd be performing long steady pulls rather than forwards and backwards activity such as would be seen with a dozing operation, then operator ease and comfort, and productivity for that type of operation is not a consideration. That heat you feel from the transmission ultimately comes from the fuel you're burning and does not constitute effective work done. Both transmission types produce heat and I don't know if one produces less heat per unit of work done but I would guess that a direct drive machine might theoretically produce less heat, but it would all depend on a bunch of factors such as gear power transfer efficiency, availability of torque convertor locking, lube/pressure pump efficiency which would also be affected by transmission condition / wear, oil condition, etc. etc.
Perhaps Cat published a comparison based on lab and field tests?