Have replaced theromastat, radiator only blows out cool air not warm

If you know for sure the thermostat is working, it could be low on coolant and has air pockets in the system. Only one radiator hose should be warm until the engine reaches normal temp, and both heater hoses should be very warm.

The first thing I would verify is that there are no air pockets in the cooling system. It can look full but actually have air in the system from being drained.
The next thing would be circulation thru the radiator. Then a blockage in the radiator hose or the block.

check and make sure the radiator is full of antifreeze take off the radiator cap and top off the radiator then take your hand and cover the hole where the cap goes and squeeze the top radiator hose a few times to help it go down that way if there is a air pocket somewhere it will help push it out when you thank your done top off again and replace the cap and try

Air can be purged. While your engine is cool remove radiator and reservoir caps. Place funnel in radiator. Turn heat to the highest position and start vehicle. Add coolant to radiator as needed while vehicle warms up. You should see bubbles coming out of radiator. Fill reservoir to between cold and hot fill lines. Replace caps when bubbling stops but before coolant temperature reaches normal operating temperature. Never remove the radiator cap until engine has fully cooled down.

When the coolant flush was done, did you have the thermostat changed as well? I would have the thermostat replaced. If the temperature gauge was reading properly, but you still had warm, not hot air, it would lean more towards the heater core being clogged, but that deosn't seem to be the issue your having, so i would go with the thermostat replacement. And whereever you have the repairs done at...make sure they fully bleed all the air out of the cooling system, this could also cause poor warm-up / heating problems. Hope this helps...

you may have a blocked radiator means that coolant is not flowing through cooling system

change therostat and bleed air out of coolent make shur the cooling fan is working

Follow top radiator hoze to the engine block. The item it is attached too is the thermostat hosing. Remove coolant for the radiator. Remove theromastat housinf. Remove theromastat.Clean all casting surfaces for new gaskert. Place gaskert and sealer on cleaned surfaces as well as the new thermostat in exactly ther same position as the ond one came out. Tighten bolts evenly. Refill the radiator with the coolant. Add extra coolant to replace what was lost. 

I think you are on top of your problem,,you dont need any one elses advice.
Complete rebuild of the cooling and heating system,, simple.

The system just needs to get all the air pockets out if you switched everything like you said look around where the radiator hose meets where you put the thermostat in, there should be something on the lines of a little nipple with a 8 mm bolt on it i will have to pull up the exact setup of your Taurus but its the same general concept your car is fine you just have a big air pocket , what else you can do is while its cold right now and the car isnt running is to go take the radiator cap off the radiator and see if the antifreeze is low now that the car has cold down since you last ran it. If so feel it up top it off in the radiator and it might hurp it self and remove the air pocket all on its own... If you need any more help feel free im always on here id be glad to help more in detail once you try that and look under the hood for the bleeder ( the thing with the nipple on it) Also if you could please rate me i would greatly appreciate it.

Thanks,
Steve