Why would one correct for the heat island effect? It is in fact the truth; the climate in cities can be quite different from the suburban areas (same with weather, if the heat island is dry it ends up diminishing or even killing off a lot of rainfall, or it can feed a system if the ground is saturated and it's hot, adding a lot of additional humidity in a localized area).
The heat island is a true localized climate (sometimes temps are over 10F lower only 10 miles from the city of St. Louis), like some desert/tropical forest areas in the Galapagos Islands where the environment transforms after a couple of minutes of elevation change when driving (on the main island, the name escapes me).
I would seem to me that you shouldn't adjust any individual values, and that the average for a larger region should be the basis for science.
I would agree that adjustments would be needed if you know that the data is inaccurate to begin with. Determining why the data isn't accurate and how to adjust is the devil in the details. And great fodder for deniers.
For the record I believe in man-caused climate change on a global scale. We're dumping considerable amounts of CO2 stored for millions of years back into the environment (which can and is leading to larger methane releases that only exacerbate the problem). Coral is dying, we are destroying ocean ecosystems via over fishing; but at least we realize and recognize these things now. The 1960s/70s were bonanzas of "because we can" with little or no consideration of systemic effects (especially with regards to food, "let's put these chemicals in the food, it will be better"). We're better on that front, except for India and China (and Africa), or half the population of the Earth.