Just to clarify, you had zero heat at all? There is a known issue where Ford released a TSB regarding one of the actuator doors wouldn't switch over causing cold air to blow out. But this normally caused the driver's side to blow cold and passenger side to blow normal/hot.
This would be the first that I've heard of both sides blowing cold air. Being that you have a 2011 and the TSB I included below is for 2011 models, I'm inclined to believe this is your issue.
The part lists for $17.02 MSRP and about $9 through discount Ford sites online but then you add shipping. With 1 hour of labor you are looking at roughly $125-$150 for the repair (booked at 1.1 hours plus the part).
12-1-8 DUAL AUTOMATIC TEMPERATURE CONTROL (DATC) - BLEND DOOR ACTUATOR INOPERATIVE
ISSUE:
Some 2011 Explorer vehicles equipped with DATC system may experience unresponsive temperature change when requested and/or erratic temperature change.
ACTION:
Follow the Service Procedure steps to correct the condition.
SERVICE PROCEDURE
Remove temperature blend door actuators, refer to Workshop Manual (WSM), Section 412-00.
Suspect parts have a black cover and new service part has a white cover.
Remove alignment feature from new actuators. (Figure 1)
Figure 1 - Article 12-1-8
Support actuator flange so there is not stress on the actuator body. (Figure 2)
Figure 2 - Article 12-1-8
Drill out the 2 webs with a 3.17 mm (1/8") drill bit. (Figure 3)
Figure 3 - Article 12-1-8
Install new actuators, refer to WSM, Section 412-00.
Reprogram the Heating Ventilation Air Conditioning (HVAC) module to the latest calibration using IDS release 76.04 and higher or 77.01 and higher. This new calibration is not included in the VCM 2012.1 DVD. Calibration files may also be obtained at
www.motorcraft.com.
PART NUMBER PART NAME
AA5Z-19E616-C Motor Assembly
WARRANTY STATUS:
Eligible Under Provisions Of New Vehicle Limited Warranty Coverage
IMPORTANT: Warranty/ESP coverage limits/policies/prior approvals are not altered by a TSB. Warranty/ESP coverage limits are determined by the identified causal part and verified using the OASIS part coverage tool.
OPERATION DESCRIPTION TIME
120108A 2011 Explorer: Replace The Blend Door Actuators Includes Time To Modify The New Actuators And Reprogram The HVAC Module (Do Not Use With Any Other Labor Operations) 1.1 Hrs.
DEALER CODING
BASIC PART NO. CONDITION CODE
19E616 42