The problem is our current data sets do not have any indication of longer term cycles of century and millennia length.
Of course they do. Relatively short-term (centuries and low millenia), you can get quite accurate temperature data from the plant record - things like tree growth rings, pollen composition and distribution, etc. For somewhat longer term (tens to hundreds of thousands of years), and higher elevations/latitudes, you can extract temperature record from the isotopic composition of ice and from stalactites/stalagmites. Even longer term, you get temperature data from isotopic composition of sedimentary rock formations.
As you go further back in time, temporal resolution decreases - first you average over months, then years, then decades and so on; it also gets harder to calibrate the temperature scale, and to establish a continuous temperature record at a given location; you may also have a quite accurate reading of the ocean temperature, but a much more uncertain data on the atmospheric temperatures; and so on.
Sure this is hard work, and it requires a lot of specialized skills and knowledge, and frequently expensive equipment. Occasionally, it is necessary to correct some of the temperature record as new and better data or analysis technique comes along - this is all a part and parcel of the scientific process. Nonetheless, claiming that our knowledge of the Earth's temperature record starts with the invention of the thermometer is just plain ignorant.