Kathryn,
It is possible to derive precise measurements. Let me put my nerd cap on more than normal: My undergraduate research thesis was on determining average temperature in a few different locations across the K/T boundary (approx. 65 million years ago) using mathematical formula derived from leaf physiognomy. In short, assuming leaves evolve in certain ways in response to environmental factors (rainfall, temperature) can correlations be established that are consistent with other data available? (Answer: Yes, but not with the precision to break new ground, especially in areas where there is not an adequate quantity of fossilized plants). Ice core and isotope analysis gives an ability to determine average temperatures. This is how we know, for example, that it was warmer in the 13th century… More interesting research (at least for me) occurs where hard science and humanities overlap: The Chinese through much of their history kept good records and the Persians were thriving during much of the European dark ages. When records do exist, do they confirm patterns suggested by the scientific evidence? Where things go wrong is with some of the modeling. After all, models can be excellent, but they can also provide examples of garbage-in, garbage-out, especially when they do not take into account such factors as solar activity.