While urban areas are warmer than surrounding rural areas, the urban heat island effect has had little to no effect on our warming world because scientists have accounted for it in their measurements.
Urban heat islands are not a newly-discovered phenomenon. Using simple mercury thermometers, weather-watchers have noticed for some two centuries that cities tend to be warmer than surrounding rural areas.
Likewise, researchers have long noticed that the magnitude of heat islands can vary significantly between cities. However, they are able to filter out those effects from the long-term trends. Overall, the urban heat island effect has not contributed very much to our warming world. Other human activities, primarily the burning of fossil fuels, are the main culprit.