I'm having flashbacks to a famous decades old climate denialism talking point heavily pushed by the Koch pro oil media think tanks.
One so famous that it was studied in depth by a prominent US physics professor [1] and (then) climate skeptic using some Koch funding.
The results of the 2013 Berkeley Earth land temperature data analysis on urban heat islands answers your concerns:
When we began our study, we felt that skeptics had raised legitimate issues, and we didn't know what we'd find. Our results turned out to be close to those published by prior groups. We think that means that those groups had truly been very careful in their work, despite their inability to convince some skeptics of that. They managed to avoid bias in their data selection, homogenization and other corrections.
Global warming is real. Perhaps our results will help cool this portion of the climate debate. How much of the warming is due to humans and what will be the likely effects? We made no independent assessment of that. [1]
and
The Berkeley Earth group concluded that the warming trend is real, that over the past 50 years (between the decades of the 1950s and 2000s) the land surface warmed by 0.91±0.05 °C, and their results mirror those obtained from earlier studies carried out by the U.S. National Oceanic and Atmospheric Administration (NOAA), the Hadley Centre, NASA's Goddard Institute for Space Studies (GISS) Surface Temperature Analysis, and the Climatic Research Unit (CRU) at the University of East Anglia.
The study also found that the urban heat island effect and poor station quality did not bias the results obtained from these earlier studies. [2]
You missed the followup. People investigated BEST and discovered it was doing the same things with the same sorts of mistakes as other climatological temperature datasets. For example they classified the weather stations at Bangkok airport as "very rural". Like always with climatology the process they used to do all this is non-replicable, so people could see the mistakes but not diagnose how they happened or attempt to fix them. Plus, although Berkeley Earth claimed UHI was unimportant, basic checks like comparing the warming of cities vs more rural stations showed huge differences.
There's also the issue that BEST has diverged drastically from satellite observations. It's not possible for both sources to be true simultaneously as they claim to be measuring the same thing.
It's not hugely surprising that they claimed to investigate these concerns and then simply duplicated the bad methodologies that were being criticized in the first place. Berkeley Earth is run by a guy who has said, amongst other things,
"I would love to believe that the results of Mann et al. are correct, and that the last few years have been the warmest in a millennium."
In the same article where he said that he observed that anyone who took issue with the Mann hockey-stick history rewrites were attacked and people had engaged in mass resignations simply because papers disagreeing with it were published.
There's a fundamental philosophy of science issue here that can't be resolved with the "one more study" approach. Climatologists don't attempt to improve their source data quality. They don't build and operate weather station networks, they rely on others that were built for other purposes. Although the changes they claim to be monitoring are very small (like 0.1-0.2 C per decade) they don't set up the instruments they need to obtain such precise and accurate measurements. Instead they suck up data from literally any thermometer they can find and then apply algorithms that they claim correct the bias and corruption. This isn't scientifically valid. If scientists have doubts about their source data they're supposed to use error bars, but when did you ever see a temperature graph that had error bars? They never do because many of the stations they use report uncertainty intervals of anywhere from half a degree C to even 5 degrees C. These CIs are much wider than the size of the claimed trend and would thus destroy any ability to detect warming from the ground station network. So, they rely on this algorithmic approach, but that isn't convincing due to how frequently they decided their previous algorithms were wrong and rewrite the history of the climate.
One so famous that it was studied in depth by a prominent US physics professor [1] and (then) climate skeptic using some Koch funding.
The results of the 2013 Berkeley Earth land temperature data analysis on urban heat islands answers your concerns:
and [1] https://en.wikipedia.org/wiki/Richard_A._Muller[2] https://en.wikipedia.org/wiki/Berkeley_Earth