In living memory means in a recent enough time as to be remembered by people who are alive today, which is the same as saying it's the hottest summer in recent history.
Context: "It's the hottest summer in recent history 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?