Excactly. It is the TA3255 chips "internal" temperature I like to lower and this needs a medium called "thermal paste"Right - but that wont change the surface temperature of the device. It will only impact the internal temperature of the chips.
Power consumption is the same regardless of whether thermal paste is installed. It is power consumption that dicates how hot the amp gets overall. Paste is about getting power out of the chip with minimal chip temperature rise.
It helps to "cool" the inerts of that amp with the help of thermal paste and the heat sink (casing)...
That's, what every manufacturer is after, in't ist ?