a graduate student at Berkeley gave a presentation on exactly this topic, a few years ago. From first-hand viewing, they used maths to determine range of effect

a graduate student at Berkeley gave a presentation on exactly this topic, a few years ago. From first-hand viewing, they used maths to determine range of effect of the heat entrapment in urban enclaves, at several scales. It was rigorous enough for the serious science in the room, and was well-received. The result is basically as someone else said -- local effects are very large, but regarding the whole climate, not a driver basically.