The ice cores are fairly reliable: https://www.bas.ac.uk/data/our-data/publication/ice-cores-an...
The link does not at all answer the main question for beginning to evaluate a temperature reconstruction of 125.000 years, that is: how well are the global annual temperature estimated from ice cores, for the years where we do have instrumental data?
By measuring the ratios of different water isotopes in polar ice cores, we can determine how temperature in Antarctica and Greenland has changed in the past.