My daughter has a 2013 Eacape SE with the 1.6l engine. It runs hot at various time. We have replaced the water pump, the thermostat, the engine coolant bypass valve, the coolant reservoir. We are lost on it. You can let it idle for an hour, never runs hot. Drive it, and it runs hot very shortly. The dash will say low on coolant, but it’s not.
The warning light saying, “find a safe place to pull over” will come on, but the gauge won’t show hot. Can anyone give us an idea on what to try next?

 

Sounds to me like you may have a air bubble in the system, jack up the front end, rhino ramps will work, take degas cap off, run engine and rev it up(while in park) for a few minutes to get the coolant flowing and if there's a air bubble it should rise to the highest point which would be the degas bottle after the front end is pointed up.
That said the 1.5 & 1.6 ecoboost engines are known for warping the heads due to bad coolant circulation around the cylinders.
I assume you've had the coolant level sensor recall completed already since you say that a low coolant level warning comes on.

 

You first have to determine if the engine is actually running hot. Are you losing coolant? If you are not losing coolant and coolant is not being forced out the recovery bottle, I doubt your cylinder head or its gasket are to blame. Connect a scan tool, have someone monitor the actual coolant temperature while you drive. Coolant temperature should be "around" 195-200 degrees when the engine is warmed up.Once you determine the actual temperature being read by the computer via the coolant temperature sensor, you can act accordingly.

 

The guy working on this car said it does push fluid out of the reservoir when it is driven, even if he puts it on the rack and just puts it in drive. But never when it is sitting idling.

 

Sounds like a bad headgasket.

 

Go buy a bottle of coolant premixed, dip your fingers in it and rub them together to feel how 100% coolant feels, let the car overheat, let it cool back down and dip your fingers in the degas bottle, coolant mixed with oil feel different then just coolant, I dont know how to describe the feeling but you should be able to feel the difference. You have to dip your bare fingers in, no gloves.
Depending on how good your sense of smell is you can smell the coolant to see if it has a hint of oil.