In living memory means in a recent enough time as to be remembered by people who are alive today, but this context is talking about the hottest summer since time immemorial which is a much longer time period.
Context: "It's the hottest summer since time immemorial and, - in these parts, that's a long, long time." Claim: "It's the hottest summer in living memory and, - in these parts, that's a long, long time."
Considering the context, is the claim true, false, or unknown?