Cities already have different microclimates - they can be 3 or 4°C warmer than the surrounding area. This is comfortable for us in the winter, but not so comfortable in the summer. On an even smaller scale, depending on their orientation, streets with tall buildings can either become canyons that are wind tunnels or else harbour stale polluted air with no movement. The buildings shade the streets below too, but not in the way that a tree canopy would. Water is drained away quickly from the hard surfaces. So, they are hot, dry, but sunless places, inhospitable to living things, unless we add trees and parks, green walls and green roofs.
Certain parts of North London with an ethnic population from warmer climates, have air conditoning units on every residential house, as well as on offices and shops. Walking by on the streets outside, you can really feel the heat being pumped out of these houses during the summer, and it is quite uncomfortable on some of the already hot days that we've had in recent years. I expect that even more people will get air conditioning for their residential houses in the future, due to rising summer temperatures, working from home, and higher summer temperatures over a longer period of time.
So, yes, higher temperatures in built-up areas do affect the climate in a bubble surrouning them, and while it is nothing new, heat pumps will continue to do that. They do, however, just like the air conditioning units, simply move the heat around, rather than releasing chemically stored energy. That has to be a good thing, but if you mean it isn't truely renewable energy, well it is being "collected from renewable resources that are naturally replenished on a human timescale" and so technically it is.
Also, the "city block sized heat pumps" that I have heard about are using warm water from flooded coal mines in places like Durham. I assume that the Cornish example in the report is using Tin mines. So, the heat is being taken from deep underground, much deeper than any tree roots. I can't see that being a problem. The idea is more like having a very low energy geothermal plant.