2001 Ford Taurus No Heat?

I have a 2001 Ford Taurus SE with no heat? The tempature gauge in this car fluctuates between the middle and cold. It never stays in the middle like it should, it's always in-between the middle and cold. It will blow out very medium heat when I rev the engine up but it's not that hot, It usually stops doing this when I just let the car idle. I did have just the heater core flushed about three months ago. Can someone please tell me what could be wrong.

Thermostat is likely sticking open. Replace the thermostat, flush and bleed the coolant.

Might be thermostat needs replacing

Heater core plugged or the thermostat needs to be replaced. I'd guess the thermostat needs replaced.

On those types of Taurus's, while the heater core can get clogged, it's more likely an issue with the heater hoses. They are a combination of preformed rubber & steel lines that have many bends in them and the steel tubing sections are notorious for collecting sediment and clogging up.
Your thermostat seems to be faulty, so get that changed and have those heater hoses either flushed out or replaced.
If this is done right, all will be nice & warm inside the Taurus, as it should be.

Thermostat is likely stuck open - had a Focus that did that and didn't heat the engine properly enough in cold weather to make the heater work efficiently. Probably the cheapest and easiest fix and given your description almost certainly the cause. Yes heater cores can clog (but not likely as the construction is the same as the radiator).

Most likely you probably need to flush the heater core again. I had to flush mine four times before I got all of the junk out of my cooling system. Also, I was leaking coolant from the timing chain cover. I replaced the timing chain gasket myself because the mechanic wanted $1100 to fix it.

When the temperature gauge fluctuates there's air in the cooling system due to a leak or bad head gasket. Have you even checked your coolant level in the radiator yet? That's the first thing you need to do.

Start by replacing the thermostat and ensuring you have enough coolant with no air in the system. Cheap to do and doubtless will solve your problem.

2 issues .1) the thermostat is probably bad. 2) might be low coolant.

You have a control on your dash that says "cold - hot". Ever wonder what that controls? Pop open the hood. You will see 2 one inch hoses go into the firewall. Both goes to the heater core. One line is IN and the other line is OUT. It doesn't matter which is which, but on one hose in the engine compartment there's a "THINGY" on it. This is called a GATE. It is basically a door that opens and closes the tube to allow coolant to flow through, or not to flow through.(in the summer, no one wants heat in the car)
. This gate has an ARM (on it in some makes of Gates) that has a hole in the end of the arm so a steel wire can go through it to the Hot-Cold control lever inside the car.
. Sometimes the ARM breaks off, sometimes the steel wire becomes disconnected and is just floating in space so that if someone moves the inside control lever you can see that the wire is not connected to anything and just goes in and out. Having a second person in the car just to move the lever from Hot - Cold and you looking under the hood can see which wire it is. This is really stiff wire so you have to disconnect the gate from the heater hose to thread on the wire through the hole to the middle of the zigzag and leave it there and hook it back up to the heater hose. Then you have control of the flow of the coolant to the heater core. Maybe what is happening right now is a bit of coolant gets in because the gate is partially open.
. But when you said you have to rev it suggests you are low on coolant. The heater core is the highest point in the system, so you have air in the system. On a cold engine check your coolant levels and fill it up and check all hose clamps for tightness. Even turning the screw 1/4 turn is tighter than it was… Meaning that maybe coolant was leaking past that clamp as all rubber hoses shrink in thickness over time. You have about a dozen clamps(maybe more) to check. The heater core is not leaking, the hoses going to it are not clamped on as tight. The gate itself (as it is a moving part may also be leaking… Which you can see as coolant would be slowly dripping outside the gate into the engine bay)

If this is more info than you can handle, take to a mechanic… Or wait till summer in a few months and you don't have to wear the heavy coats.