It's not horrible science. It's very simple analysis and maths.
Graphs are used to answer a question: "what is the relationship between these objects" or "how are these things changing" or "what is the trend in their rates of change".
In this case, we're less concerned with the actual temperatures at the individual stations than we are with how they're changing over time. So, there's nothing wrong with adjusting and merging them together like that.
Think of it this way: what if we were to remove the temperatures from the left side of the graph, and instead plot the temperatures as a series of differences? i.e., temperature station 1 has +5 at one point, -1 at another point, and so on.
You could plot the changes in temperature for a number of stations that way, all on the same graph, and it would make perfect sense.
That's really all they're doing.
As for measuring temperature at airports: if there is such an effect, then it will produce uniformly higher temperatures, but it will not affect the rate of temperature changes -- so, again, as long as the question is, "how is the temperature changing", taking measurements at airports is acceptable.