It is not done for better temps. It is to protect the cpu die. Amd used to have open die designs, back with socket A. A lot of people killed their cpus when installing a heatsink. For the cost of adding a heat spreader is rather low, and prevents death of a good cpu with improper installation of a heatsink.
It has admittedly been a while, but I'm pretty sure that Intel's stated reason for moving to integrated heat spreaders was to help with heat dissipation. The core cracking thing was a problem and the IHS was a solution to it, but all the comments Intel made at that time were in relation to cooling the smaller and smaller dies. Hence the name integrated heat spreader and not integrated core protector or something. I was trying to find the link to the initial IHS announcement, but can't find it now.