I flushed out my heater core twice. There is a noticeable difference (hands at center vent now can get burnt) after care is up to temperature.
I just want to know if there is a chemical I can inject into the core via the entry and exit tubes that will dissolve anything more that's not being flushed out.
They make chemical descaling solutions that designed to be used in cooling system - most are caustic in some manner (highly acidic or highly basic), depending on what coolant was used in there previously.
Did you notice what sort of debris was flushed from the core - was it like a mud/sand thing or more like a gel/something in solution? For attacking just the core, chemical descaler will be fine - just note that they can be so effective, that if there was a pinhole leak that was plugged by some deposit - they will cause that core to start leaking. Usually recommended to pull the core, have it cleaned at a shop, then immediately pressure tested.
Might be perfectly fine - but you don't want to go through all the trouble of descaling, only to find out that it leaks like a sieve under the dash.
I actually didn't see anything noticeable coming out of the core when I flushed it the first time. It was from a garden hose of the high-pressure "full" setting.
What are the names of these descalers and where can they be purchased?
Probably the two most common automotive ones are Prestone Radiator Flush and Cleaner and Gunk 10 minute radiator flush. hey run about $5-$10 a bottle, depending on where you get them. I've even heard of some people using CLR or similar household cleaners in the cooling system - but I'd be hard pressed to use those. Will very aggressively eat aluminum and soft metals.
So I could just block off the lower core hose while pouring that stuff in through the top hose, then let it sit for about ten minutes?
Yup, see of that loosens anything in the process. Make sure to flush it with plenty of water - garden hose with tap water would be OK for this, need a little pressure to push any contaminates out. What little tap water is left in the core, the additive package in the rest of the coolant should be able to buffer out pretty easily.