All of the data collected comes down to temperature calculations, the measurement of temperature has not changed during that time period, so why would calculating differences in it be difficult?
There have been recorded temperature readings going back to 1880 that they're using for comparison.... what do "tree rings" have to do with it? They may be used going back for long periods, but there have actually people recording the temperature since 1880, and that is the data used for comparison.
I don't see a real question here really..... how do you compare the temperature in your freezer today to the temperature in your freezer 5 years ago -- if you've been tracking that temperature all that time, you simply pull up the numbers and do the calculation.
Unless the standard of measuring temperature has changed (it hasn't) it's not a big deal.
From the NOAA website:
"Although NOAA was formed in 1970, the agencies that came together at that time are among the oldest in the Federal Government. The agencies included the United States Coast and Geodetic Survey formed in 1807, the Weather Bureau formed in 1870, and the Bureau of Commercial Fisheries formed in 1871. Individually these organizations were America's first physical science agency, America's first agency dedicated specifically to the atmospheric sciences, and America's first conservation agency. Much of America's scientific heritage resides in these agencies. They brought their cultures of scientific accuracy and precision, stewardship of resources, and protection of life and property to the newly formed agency. "
So why, if the agencies that eventually became NOAA were formed well before 1880, would you think they would need to resort to "tree rings" as a measure of temperature going back that far? They can compare back that far, because they actually have records going back that far.