Heat not working, no hot air

I heard that you can backflush your coolant system to attempt to clear out the heater core or other problems. I know how to flush the system but I'm not exactly sure how to back flush it. Would you just hook up a garden hose to the in and out hoses through the firewall and run some water through it?

Thanks again for all the help.

I am also experiencing a problem with the heat in my 88 Lincoln although I have limited heat which after 15 or so miles just blows out semi warm.
With regards to your heater core, I had my replaced several years ago as the previous owner obviously failed to regularly flush out the system and it began to leak after I flushed the system and removed the rust.
Unfortunately this is not an easy job as you need to dismantle alot of the dashboard in order to access/remove/install a new core. The core itself isn't expensive but the time involved is. I dismantled the dash, had everything disconnected but was unable to get the core out. Finally took it to a repair shop specializing in heating systems. I think another set of hands would have helped trying to pull it out from under the dash. You will need the manual if you are willing to attempt the repair yourself as it is a little complex.