Before you make assumptions this isn't about the EATC system.
I have a 05 Lariat 5.4 with the EATC system. EATC works fine. New blend door actuator last year. I've never had hot air though. Occasionally warm, but never hot. When it's 30 outside I wear my Carhart with the heat on full blast and the seat heaters on, and stay that way for my 45 minute commute. Get the idea? Anyways. I replaced the thermostat today, hoping that might've been part of the cause. However, it still only blows warm for a moment before getting cold. I'm thinking heater core and hoses. I found the input hose but cant find the output hose. Looking in my Hanes manual, I'm not interested in disassembling my interior. Is it possible to do without doing that? Any advice would be great.

 

You'll need to check the inlet and outlet hoses for temperature. If HOT coolant is not circulating through the core at the needed volume, you'll never have full heat.

The core's tubes come through the firewall side-by-side, you'll just need to access them or the hoses that connect to each.

Most likely, you have either a restricted core or a weak pump (eroded impeller).

 

Many vehicles have a valve in the hot line to the heater core - I don't know if yours does. Other than that you need to do what the above post said and determine if hot coolant is passing through the heater core. Unfortunately I don't know what the EATC system is but I assume its sort of a climate control? Operating it manually, change the registers to the dash so its easier to feel the temps and blower force while troubleshooting.
I'm assuming on an '05 that you have already changed the coolant twice (every 5 years). If you haven't, and if you have used the wrong coolant or non-distilled water to mix it, anything could be wrong with any part of the cooling system including the heater core.

 

A blast of heat followed by it getting cold is a clear sign that not enough coolant is flowing through the heater core to keep it heated, or your blend door, although working isn't adjusted properly and is allowing cold air into the mix. You really need to feel both hoses to see if both are to hot to hold or not.

 

I thought of something else that is a weird condition but has happened plenty of times - you have a pressure leak like a slightly loose or cracked cap on the surge tank. You don't see a coolant leak because you're only leaking vapor, but it prevents the system from drawing the coolant from the tank when it cools. Over time the coolant level will go down, and sometimes it leaves the heater core 'high and dry'.
If you have a radiator cap, you just check it cold and see that the radiator is full and the surge tank has the normal 'cold' level. Furthermore, you should mark that cold level and then drive the truck for a half-hour or so, bring it back to the exact same spot and check the surge tank level, which should be about an inch higher or at the 'hot' mark. Mark this level too for future checking. If it passes these tests, you can be assured that it is full of coolant and the system is tight.
If you don't have a radiator cap all you can do is check the surge tank cold and hot levels - if they are changing as-expected, the system is full and tight.
Most owners never make the surge tank/radiator cap check and it really can save you a lot of trouble.

 

I've heard that some 5.4 engines have a valve that cuts on and off the flow to the heat core. How can I tell if my truck has this and is there a way to make it open manually?

 

Look on the heater hoses.

 

No valve in these. But there is a flow restrictor that is the source of lots of issues. When these trucks were new the dealers pulled a lot of the flow restrictions due to performance issues. I pulled mine in my 2006 when it was new. Look at the heater hose lines and you will see a grey clamp on the hose near the manifold and that is retaining a plastic flow restrictor. Cut the clamp band and remove the restrictor with a pick.

 

Is the flow restrictor on the hose that doubles back in itself?

 

There isn't any heater hose that doubles back.

 

I've located both of my heater hoses. At 2,200 RPM they're both warm, and I get some warm air in the cabin. At idle, one matches temp with the upper rad hose, the other is cold, like the air blowing out my vents. I verified my blend door actuator is working, so no worries there. I'm thinking flush both of the heater lines and the core and hope for the best, but if not, is there an easy way to pull the heat core like in the early 90's models where you can pull it out the glove box or do I actually have to pull the dash?

 

take the heater hose loose and connect to a garden hose.. BLAST it out... You can also fill with some cleaner or lime / calcium dissolver and let it set and work, then wash out.

 

Definitely a restricted heater core. You're on the right track.

 

Did you pull the restrictor out? The heater core is a 10 hour job to replace.

 

I looked into the restrictor, and from what I understand it's there to protect the core from being overpressurized by the engine and causing it to burst. I'll check it and make sure it's not clogged, but I'm going to leave it in. Is it safe to pour CLR into the core?