Here's a map showing the results for all of North America. I created a smoothed contour map rather than showing all the points, because there are so many stations in the lower 48 that all the markers overlap. We see that Fairbanks temperatures do indeed have a modest negative correlation with temperatures in parts of the southwest US at this time of year, and there is a small positive correlation with the northern Plains and upper Midwest.
Below are the maps for each month of the year (click to enlarge). A surprising result is that the scale of very good correlations (R>0.9) across Alaska and western Canada is greatest in September; I would have expected this to occur in winter.