Different CPU assemblies have different thermal signatures (the clarkdale actually has two chips with different heat signatures on different sides of the CPU assembly).1156 coolers are made for Lynnfield
, just because it came before Clarkdale, and it was also the hotter running CPU since it had 4 cores. Clarkdale had 2.
In many situations though, manufacturers just added 1156 support to existing 775 and 1366 coolers.
For every dual chip CPU there has been a single chip counterpart:
Smithfield & Prescott, Presler & Cedarmill, Kentsfield & Conroe, Yorkfield & Wolfdale, Clarkdale & Lynnfield (different nm).
The CPU's older than Lynnfiled had chips that were more square shaped, meaning that when placed in pairs, they had quite a different layout than the single chip version.
Still, I never saw coolers optimized for one or the other. There are exceptions like AMD's huge dual server chips.
Besides, it's not like Clarkdale (Westmere) looked that much different just because it got two chips.