According to accounts of Kozyrev Experiments , they were picking up Sumerian symbols in the past. The cannot be more then \(5 \sim 6\,\,^oC\) different between the ambient air and the ground.
If this range of temperature brings back the past from 6123 to 3773 years, then one degrees Celsius difference between the hot and cold points will bring back the past from roughly a thousand years ago.
Very fine temperature tunning will be needed to land precisely at a particular point in the past.
Since the background time flux is already downwards (Earth being one big time particle), the recent past may just be accessible only when the hot and cold points are reversed; when the time flux produced counters the background time flux.
All in all, not a difficult engineering feat to be tested immediately.