Engine stumbles when cold

When I first start my engine when its completely cold, it will stumble and run rough for about a minute of driving. Than as it gets warmed up, it smoothes right out? I've cleaned the throttle body with sensor safe fluid, and have also changed the plugs to Champion Truck Plugs.

Any suggestions.

Also one other thing..............it starts really hard after its warmed up and has been shut off for about 20 minutes. But if I turn the key off and on again it fires right up.....fuel pressure? Fuel Pump?

Any other thoughts?

Thanks.

What year is it? When you cleaned the TB, did you remove and clean the Idle Air Controller (IAC)?