It isn't so much that the overall temperatures will change too much when averaged out, that would relate more to the slow down/stopping of the AMOC.

First order effect, this would mean that you get less predictable weather events. Essentially, heat domes and artic blasts become much more persistent, sticking around for weeks or even months (worst case) rather than just brief periods.

Second order, A month long heat wave can kill a lot of crops followed by a month low wet spell that can completely flood the same area.

Third order effect, In metropolitan areas this is an inconvenience. For the food system, this is deadly.

Forth order effect, a fragile food system that feeds the metropolitan areas - things get dicey fast. Tough times, tough leaders, rise of authoritarianism etc. May you live in interesting times.