Here's a few suggestions when dealing with heater core issues.
No1 test the anti-freeze with a anti-freeze tester that most Wally Marts etc carry for around 8 bucks or so.I f the tester and the coolants colour indicates it's worn out or dirty change the coolant in the vehicle by using the rad's drain plug , adding water steadily and reflushing the rad till it basically comes out as water mostly, then add the coolant mixture.Make sure unless you live in the very severe coldest climates not to really mix the anti-freeze and water more then 50/50 or to about -45, plus don't dump coolant on the ground it's sweet taisting to animals and will kill dogs and cats etc.
No2 Once proper coolant mixtures and levels have been established cold start up the engine with no blower motors on at all then squeeze the top rad rose or thermostat house.
If no pressure builds up within a few mins or the engine has reached it's normal warm up temperatures then more likely the thermostat isn't the right one for the engine or that season of the year or the thermostat is warn or faulty.be sure you check the vehicle under the hood and underneath the vehicle for any leaks , from the engine or any of the rad hoses or rad or even the over flow container etc ,
No3 if the pressure builds up and no leaks then as the engine is still idling listen and watch from a safe distance for the fan to enage as you realize the hose, plus go into the vehicle and set the heat on high with full blower motor on. Then go back under the hood and reach up to the two smaller heater core hoses and feel them are they both getting hot , check the temperature gage to see what the engines temperature range is at and go back to see if the fan has engaged or the two hoses are hot.
If only one of the heater core hoses is only hot then that indicates that the heater core maybe clogged or faulty or that there is a air lock in the heater core unit's system.If the fan never engages with engine fairly worm or hot check the rad fan's fuse under the hood in fuse box and the fan relay, plus check the temperature sensor and rad plug in connections, plus visually check the wires for damages or if their fray or bare or burnt etc.
No4 with blower motor on high still doors closed is there any scent coming from the venting system that is irrating if so the heater core is faulty and requires replacement, plus if you turn the windhield defroster on high does a scum or a greasy type of stuff appear on vehicles interior part of the windshield, if so again it says heater core needs replacing asap.
No5 If the two hoses did get hot or say not hot enough then you may require a better temperature range of thermostat or the heater core maybe slightly clogged etc.
No6 if you suspect the heater core is clogged or air blocked then with the engine cold all coolant levels at the proper levels , disconnect the two small heater core hoses , switch the two hoses around and be extra cautious bec the shafts that hold the hoses onto the heater core are mostly made from plastics.Once their switched around and on firmly start the engine up let idle awhile then turn heater on and allow it to run a few mins while checking the temperature gage in process then shut engine off , allow the engine to cool to a comfortable temperature and switch the two hoses around again and recheck the system again with engine idling.You can also force water or air through the heater cores hose connectors and keep checking once you've flushed the heater core for that nasty scent or that gummy greasy stuff bec if that appears you know the heater core was clogged but isn't anymore and it's no good.
Hope that helps and best of luck.