A while back I had an issue with the no heat thing as well. I have replaced a few heater cores in the past on other vehicles (for the record, never do one on a 99 Taurus, total PITA) and so I decided to replace mine. It wasn't too bad of a tear down and replacement. Just be carefull not to crack any plastics. After I put the new core in, everything ran great.

TIP for those who don't know: A way to tell if the heater core is leaking is if there is moisture inside your vehicle. Example: windows fogging or frosting from the inside or if you passenger side floor board is wet. Also, (may just happen to me) but I get really congested and have a hard time breathing from inhaling the coolant vapors. When that happens I know for sure it is the core.