Q: Very hard staring after engine cools off

This may be a result of a cold start fuel supply issue. When you start your car when it is cold and turn the key to on, the coolant temperature sensor immediately reads the temperature of the coolant and relays this to the computer indicating that the coolant is cold. The computer then knows at this point that it needs to enrich (add more fuel) the air/fuel mixture at startup due to the change in air density. When you start the car, you will notice that it idles high for a period of time until the engine warms up. This is the enrichment cold start process. This is done with what is called a cold start injector which injects more fuel into the motor until the engine reaches a specific operating temperature. The computer simply feeds a little extra gas through the fuel injectors to start the engine and then maintains a certain amount of fuel supply to the motor until it is warm. I would recommend having an expert from YourMechanic come to your location to take a look at your vehicle and diagnose your cold start issue.