I'm not sure where the heat transfer is occurring that makes the two firewall hoses the same temp (to touch) when the valve is closed, but the fact that I get no hot air when the valve IS closed shows not much if any heat is conducting to the heater core. The valve is all metal so it will even conduct heat.

92 Montero LS 3.0L V6 Auto, Stock, Original owner, 185,800K miles