Each monthly update of V4C (corrected) changes past results as well as adding the new monthly temperatures. This is due to their homogenisation algorithm. I had already noticed that V4 gave warmer results than V3 but found that the uncorrected data agree where stations overlap.
This means that the expectation value for the temperature difference between two nearby stations is changing with time. This then affects any “adjustments” made to current and past measured values by assuming these stations always move in temperature synchronously. The end result seems to maintain warming trends. Here is a comparison of V4C and V4U.
There is also a significant difference between V4C and V4U since 2015 in the annual temperature values.
Nick Stokes uses the unadjusted data for TempLS. I am tempted to do the same or at least calculate both to get an estimate of uncertainties. There is a significant difference between the two in recent months.