I've built a bunch of 2127cc and 2174cc B20s, mostly using the earlier blocks, and have not had overheating problems. The later blocks do not inherently have more metal in the cylinder walls -- that varies quite a bit from block to block in both types.

What makes them run hot is the very thick big-bore head gasket. If you don't cut down the block deck to compensate, the head is so far from the pistons that you get very poor squish/quench characteristics. This results in a slow burn rate, allowing energy that should be going into making power to go into heating the head and block instead. It's like running retarded timing, even if you advance it to the point of pinging.