Everything you've said points to insufficient volume through the heater core. The second heater hose really won't be noticeably cooler than the feed hose. When it is, it's because too little hot coolant is going through the heater core, and what is getting through has plenty of time to be cooled down. I think there has to be a restriction somewhere. As I recall, you said there's a new heater core in there already. Still, I would disconnect both hoses, then run water through the heater core, then both hoses, with a garden hose. The water must flow easily through each hose without building pressure and spitting back as long as the radiator cap is off. If you find the water doesn't flow through one hose, check if it's hooked to a metal pipe pressed into the intake manifold. Those are made of very thin steel, and when they corrode, a part of it could flop over and block coolant flow.
Sunday, December 15th, 2013 AT 5:46 PM