How do they handle increasing rock density and compaction with depth? For example, shales may lose some of the layers of water between clay platelets with compaction. Did they measure thermal conductivity of the rock with depth? Hopefully they did.
If rocks become more conductive with depth and the effect is not taken into account, temperature should curve upward slightly with increasing depth, making it seem like a record of past colder temperatures.
Good questions, and I am utterly unqualified to answer them. But the Web page that I found (link below) provides a lot of information that may help.
Temperature Measurements in Boreholes: An Overview of Engineering and Scientific Applications
The section on paleoclimatology indicates (via references) that this aspect of borehole temperature logging, which is a common measurement, has been examined since 1923.