Why is my car hard to start in the morning?

Try turning the key to the on position (no crank) for ten seconds and then off. Repeat this 3 times and then try starting the motor. if it starts right up you've just diagnosed a bad fuel pump check valve. The bad check valve lets the fuel pressure bleed down over night. The computer shuts off the fuel pump in 10 seconds if the motor doesn't start and that's why it takes so long to build up fuel pressure so that the motor will run. The fuel pump won't fail but you'll need to cycle the key 3 times to start it right away with out making your starter motor go bad faster then normal.

It would help if you mentioned year,make,model, and engine. Is it fuel injected or carb?

A bad coolant temp sensor can cause those exact issues.
The engine needs a richer fuel mixture on a cold start-up, and if the faulty sensor's telling the computer the engine is already warm, the leaner mixture makes for a harder start-up.

Do NOT put anything in your gas tank, except gasoline.

sounds to me like your fuel pump may be starting to go. I would change fuel filter first.

try holding the gas peddle about 1/4 way down while cranking it. there is some kind of temperature sensor that may need to be replaced.

could be all kinds of things

you could get somebody to troubleshoot the air, fuel and spark situation, or if you haven't done any basic maintenance on it in while you could just replace the spark plug wires, spark plugs, gap the plugs, spray out the intake with cleaner, get the fuel filter replaced, put some seafoam in the tank, stuff like that