Will a written warning increase the cost of my car insurance?

No, you will usually not see a written warning which show an increase in your car insurance. A warning is just  designed to penalize you. If you actually got a citation then yes, it would affect your car insurance. Car insurance companies regularly check your driving record to see if you've had any new tickets or other problems. A written warning wouldn't show up on your driving record, but a citation would if you chose not to contest it.