Simple answer: Today: more areas of towns, cities and villages are covered over and there is less surface water available.
The Urban Heat Effect is not so much due to "more warming". It is due to less cooling.
Fully half of earth's surface cooling is due to a mechanism called "evaporative cooling". This depends on the presence of water at the surface; often present over land in green plants. No water, no evaporative cooling. We see the effects particularly in day time, in arid regions such as the Sahara; where it gets hotter than at the equator because there's just no water there to cool things down.
Evaporative cooling happens when liquid water changes state. For example: from liquid to gas or ice to gas. We can experience the effects just after a shower before we dry ourselves. The longer we stay wet, the colder we get. Water, covering us, steals body heat and uses the heat to change state from liquid to gas.
The amount of heat needed is called the "latent heat of vaporization", LHV. When water gains this amount of heat it does NOT raise its temperature. It's a large amount of heat. For example, the LHV for 1 gram of water is the same quantity of energy which could otherwise raise 1 gram of water from 15 C to about 82 C. When green plants expire the water vapour so produced cools the plant. The physics explanation is that liquid water exists as molecular chains about 8 water molecules long (H2O)x, bound together by inter molecular forces (or inter molecular bonds), AKA "Hydrogen bonds", or "Van der Waal forces". Latent heat energy is needed to break these bonds to create lone H2O water vapour molecules. It is called "latent" because its absorption does NOT increase the temperature of the water.
(H2O)x + LHV -> x H2O.
The water vapour molecules so made are lighter than air. Over the course of about 8 days they convect up the atmosphere; and eventually condense back to liquid, or even ice, so giving up their latent heat high above us. This heat then radiates out to space.
Modern urban areas have much less water at the surface than rural areas. Roofs, roads, sidewalks, driveways, and parking lots are designed such that rain quickly flushes down the drains.