I remove both heater hoses and use a garden hose to force water through the heater core. I just send water through both ways for a couple of minutes.
It would be best to disconnect the coolant lines and flush the core after the radiator flush. This will clear any sediment from the core.
It would be in your best interest to go to bgfindashop.com and have someone in you area do the flush, back flush, for you as they clean the system. Then they do a total fluid exchange to include the heater and then add a rust inhibitor.
Probably blocked heater matrix. Best thing to do is flush the cooling system with the best stuff you can get.
Use a back flush detergent, back flush portafilter basket, and a clean towel.
The best thing to do is go to bgfindeashop.com and locate a repair shop that has the BG chemicals. They will install a cleaner then back flush the system including the heater . Then they add a fluid conditioner.
It is best to have it done professionally as they clean the cooling system as well as back flush it.
Could have a blockage in the heater core. Or simply need a coolant flush or another item. To be safe I suggest you shop around for the best price to get it fixed.
Most likely your heater core is shot. I have the same problem. One thing that you can do to get some heat is to flush the core out by running water back and forth through the heater core. To replace the heater, your talking at least 6 hours and some know how. I flush my heater core out about every month during the winter, and that has got me through the last two winters without replacing the core. It isn't the best, but is most likely better than what you have now.
"Nut" means 'best possible' so the "nut flush" would be the best possible flush.
== == The car is about 16 years old, it needs a complete rad and heater core flush, to get the junk out of it, and make the system operate better, and more effectively. A professional radiator shop can do that for you.
A straight flush is the second best hand.
Considering that General Motors has several class action suits against them in regards to Dexcool (pink antifreeze) I would flush using the green antifreeze. The best thing to do is go online to bgfindashop.com and locate a shop near you to flush the system. They will add a cleaner and run it then do a reverse flush that will remove all the antifreeze from the system including the heater. Once that is completed they will add a conditioner.