I previously looked into this. It has a small warm bias which peaks from May to July. Maybe on the order of about 0.4F or 0.5F warmer than the average of maximum and minimum, but reaching as much as 1F during the long day period (i.e., May & June).
Keep in mind, this period predates even standardized time zones let alone daylight saving time. Time was measured in local solar time (LST), where noon equaled the time where the sun was at its peak in the sky directly overhead. For practicality, official time would be kept at one site for a city or region - perhaps a courthouse.
Detroit, owing to its location in the western part of the eastern time zone, is offset about 40 minutes from solar noon under standard time, and 1 hour, 40 minutes under DST. So the morning observation would have been taken around 8:40 EDT, so it doesn’t do a good job capturing the morning low. The inclusion of a 9 pm observation (which would actually be as late as 10:40 EDT) helps to mitigate this somewhat but does not completely eliminate the warm bias. In the wintertime, the 7 am observation (~7:40 am EST at Detroit) is pretty close to sunrise and less biased. This is the main reason for the strong seasonal effect of the bias.
The Smithsonian later changed the formula to double weight the 9 pm observation around 1870. So it became the average of 7, 2, 9, 9, which is much closer to max + min / 2, but still has a small residual warm bias by my reckoning.
Note, however, that observations weren’t always made by that standard. Sometimes only two observations were made. Sometimes, the observations were sunrise, 2, and 9 which would do a much better job of capturing the minimum. This formula would probably even have a cool bias relative to max + min / 2. However, it wasn’t as common as the other. Sometimes, the morning observation was taken even later.