Typically rates do not go up for a warning you receive by police instead of an actual ticket or citation for a moving violation, such as speeding. If it was a verbal warning by the law enforcement officer than nothing was probably written or placed on your file.
If it was a written warnings though some do go into the local files of police department computer systems. This is done so that if you are pulled over once again in the same area then the officer that runs your name and license number through the computer will see that you were given a warning previously and have not corrected your driving style so you would likely get a ticket the next time and not a warning.
Most states do not carry a fine or require a court appearance for a written warning; it instead serves as a reminder for you about your driving and that you could have been ticketed. Other states will file this warning or place a notation regarding it on your driving record.
In general car insurance companies do not look at warnings as surchargeable. Normally only violations that you are actually cited for and found guilty (convicted) of will affect your auto insurance rates. However, speeding warnings may be looked at by your insurer as a predictor of your driving habits, especially if you are starting a policy with a new insurance company.
For example when your insurer views your record and sees 2 speeding tickets in 4 years or 1 in 3 it may not look too bad to them. But if they also are able to see notations that show you have had two warnings for speeding as well than they make consider you a habitual speeder and now take notice of the actual speeding violations more and thus it could affect your rates.
In our experience, in most cases warnings do not affect your insurance because it does get sent to your motor vehicle record (MVR). There are exceptions where it can appear on you record, in those cases the infraction may affect your rates depending upon your insurance provider's rating system.
To find out if in your state warning are listed on your MVR contact your local Department of Motor Vehicles office.