Heater question

After the car warms up feel the hoses going into and out of the heater at the firewall. If one is warm and the other is cold, it would indicate the hot water is not passing through the heater core and you have a blockage. If they are both warm with maybe one just a little cooler than the other it would indicate a fairly normal flow of water.

If it's not the heater core, you might have a ducting problem under the dash, and that's a completely different problem.

Flush the heater core

Here's something that has worked for me for years (still using my original heater core). You can run a generic Prestone flush through the entire system if it's been a while, but I don't think they do much. They are so harmless to the environment the real deposits just laugh. If you want to localize on the heater core, disconnect the bottom line to the heater core at the firewall, but disconnect the top line where it connects to the metal line (this will be used to connect a funnel). I use some CLR mixed with the proper amount of hot water (might need to boil it, see directions on bottle). Pour the CLR in and just let it set a few minutes (might want too plug the bottom line while it sits). Then ram the garden hose nozzle into the top heater hose and flush the core (prepare to get wet). You can even back flush at this point if so desired. Keep in mind, if the heater core is weak, this process could finish it off, so do at your own risk (but you said you were contemplating a new one anyway). If the water is not coming out free and clear repeat the process again. The CLR should melt the deposits which is what is restricting the flow through the core.