It's not 'the' question. It's barely 'a' question. It's just been a popular one that has been seeded over every social media site for the last few years by multiple anonymous accounts - wonder who has been paying for that?
It's insulting to think that people who work day-to-day with climate data haven't thought of and accounted for that effect. We've got global, daily, satellite-based monitoring of both land and ocean surface temperatures. We can detect the local environment component of temperature change at specific sites with long time series.
That 'careful look' you wanted has been done - some people are just really 'invested' in trying to get people to discount the result. The world, as a whole is warming. The level of warming is in keeping with what we expect from the physics of atmospheric CO2. Those are facts. What, if anything, to do about those facts is still up for discussion.