They are both correct, but used slightly differently. With 'no' it is telling us that the heart is not intelligent, and using a comparison with the stomach to emphasize this. The wires in my phone are no bigger than a human hair. With 'not' it is specifically negating a statement to the contrary. Imagine the dialogue: Idiot: Chimps are the most intelligent animals. Me: Chimps are not more intelligent than humans! ..when spoken the stress is on NOT, you might even write it in capitals.

no is correct

You can use no before a noun without article and you can use before a noun with adjective (except : much, many, any, enough). For these reason : he heart is no more intelligent than the stomach it is correct.