Iknow this is a really old post but i just did this procedure and it worked very well.
My symptoms were heater not blowing very hot, and when i did turn the heat up it would blow warm for a second and then cool down really fast. I replaced the thermostat and flushed the cooling system that had been running rusty water for years(not me, previous owner). filled it with a 60/40 mix and Still no joy on the heater.
so i disconnected both heater hoses, snipped off about 2 inches and squeezed the end of the heater hose into the garden hose.
turn on the water slowly and you should get rust and crap coming out of the other hose. then reverse the flow. back and forth until full flow is observed at the other hose. I had it run gloppy rusty crap run for a couple seconds.
note: watch the pressure from the garden hose it might be too high for the core and blow a hole in it.(then again im not an expert)
finally, hook all hoses back up and enjoy the hair cinging hotness.
hope this helps