The phrase, "temperature records" in the title is not what people normally think of as records. There are not thermometer recordings.
To get the "records" for the last 12,000 years a lot of different types of "proxies" are compared and compiled to determine temperatures throughout this period.
The researchers first point to potential issues with the temperature reconstruction. There are many different kinds of proxies for temperature, including organic compounds produced by photosynthetic plankton, ratios of elements in the shells of zooplankton, oxygen isotopes in ice cores, and identification of pollen grains. [And tree ring data.]There are a number of problems with this approach. One problem is stitching different proxies together. Maybe they are not all measuring the same thing, or at the same time of year.
If one proxy for the entire period existed, it might be possible to calibrate it and use it for the entire period. But this is either not the case, or it is not trusted.
On the other hand, investigator integrity is often assumed. However, as was discovered in the case of Michael Mann's "hockey stick" model of temperatures during the Holocene, either his integrity or his math skills were lacking. His model has long since been discounted, even by the IPCC.
This is not a classic "data vs model" controversy.
The "data" are derived from the proxies and are themselves "models," although of a different sort than the "computational models" used to model the climate.
So neither the models nor the records are hard data, unlike records from weather stations or satellites.