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Heat isn't free because heat is essentially energy transfer, and energy cannot be destroyed or created, thus it always has a cost.
You might be able to try to somehow "recycle" it by piggybacking off of some heat generator such as nuclear power plant cooling water (which is not likely to be hot enough for any level of efficiency (30-40C only, usually), and also unsure of the ramifications it could have with reduced water flow and increases to flow back pressure), but it is much less likely you will find enough sustainable heat that is a byproduct of something else like that compared to just building a heat generator specifically for that. At that point, why not continue to use the technology already in place?
Not to mention building something to house that can damage the local environment, in the same way data centers do. Resources funneled to it, water diversions, noise pollution, etc. Would the pollution cost of this kind of facility be worth the pay off? Would it be less than the already pretty efficient refrigerators already in use with at least equal performance?
In reality, human existence is pollution. It is not possible for humans to live without some level of environment pollution, because humans don't really provide anything back to the environment it wasn't already getting from somewhere else. Humans are perhaps the only creature on Earth that could be deleted and there would not likely be any negative effects of the environment. Earth can take care of itself pretty well without human intervention.
There is currently so much waste heat produced by energy production and industrial processes, that for most of what the OP is talking about, the heat may as well be "free" since it was waste heat that has to be vented. Waste heat needs to be used to mitigate climate change, because waste heat is going to become an issue sooner than later.
So my background is in instrumentation and process control as an engineering technologist. In my country that means I can do limited engineering within my scope of practice, part of which extends into thermodynamics, balance of plant, steam enthalpy calculations, sizing and speccing heat exchangers, boilers, condensers, compressors, turbines, valves, and the controls for all of it.
I'm very familiar with all of this, so I can tell you from experience that these absorber plants can be bolted on after an economizer (in the case of a single effect) or you can supply higher grade heat if you're willing to sacrifice part of your economizer capacity in exchange for cooling in order to get high enough generator temperatures in a dual effect absorber.
Otherwise you have to trim with electrical resistors to get your preheated water up to the generator temp to run the absorber plant (also viable. Bolt on after the economizer and use a small amount of electrical heat to finish the missing heat to run the generator)
This isn't theoretical, you can find these absorbers already in use at combined heat and power (CHP) plants running university campuses and government/company campuses. They are already used for limited district cooling for these places to accompany heating.
The overall benefit is they are extremely low impact on the environment since LiBr is non toxic, isn't poisonous, doesn't deplete the ozone layer, doesn't contribute to GHG emissions like released butane or isobutane emissions would. It doesn't produce toxic gasses or use high pressure or exotic temperatures or materials.
It also reduces electricity demand for cooling massively. An absorber chiller runs on practically unusable waste heat that's too low enthalpy for any other use. You get free cooling and the plant is very low maintenance, ingests waste heat that would have gone up your chimney or flue, and spits out cold water. What's not to like?
The best part is they also work extremely well with renewables making them natural partners if you have a thermal sand battery paired with it. District heating and cooling can run from one very simple plant, which is going to be more and more important as our climate gets more hectic from global warming.