> By the time that's travelled 500m–1km through pipework you've lost a few degrees

you'd be surprised. If you have high flow, and the pipes are insulated and underground, then after about a week the temperature drop isn't that much. You do have heat losses, but if you have a high enough continuos flow and a big enough pipe, then it'll be low enough to not worry about, especially if the aim is heat shedding rather than efficiency.

My old flat was powered by both the 1970s boilers across the way, and more recently the massive south london incinerator. The pipe cross section was I think 40cm and at peak carried ~3-5 Megawatts of heat. I think it operated at 150c, but that could be me misremembering (this is the later version of the network: https://www.burohappold.com/projects/veolia-southwark-2-0-he... for the councils is they get a maintained heater network, which is much cheaper than doing it themselves (even more now with gas being so expensive) the power station gets to charge for a waste product and it doubles their on paper efficiency, its a win win.)