[guscost]

Prior to the satellite record historical temperature data is much less reliable, since each source is in a local area and may have different heat island effects, calibration, or quality of instruments. Additionally not as many stations were operating in 1880, which means more uncertainty about the data we do have.

Folks have tried to get around this by finding proxies for temperature (measurements that are theorized to track temperature, like the width of tree rings for example), and then calibrating that data by comparing it with the intervals for which we have reliable data (since 1970 for satellite data, or earlier for whatever thermometer data might be suitable). The long-term trends are identified and argued based on these proxies.

So to answer your question, they can calibrate a proxy using the satellite record, see what it suggests about 1880, and combine that with the available temperature data, but that's about it.