The hard part is that "daily minimum and maximum" requirement. The thermometer has to stay out of the sun continuously all day.Agreed that the maximum temperature where you actually are is a tall order. The minimum on the other hand will usually come when it is dark or at least not sunny, so that is easier to record.
Thinking back to my tours, probably in excess of 95% of the time the low is overnight or more often around dawn. In those cases looking at it when I get up in the morning yields a close approximation. There have been a few cases where the low was in the evening while still riding when there was a high pass crossed late in the day, but again it comes at a time when I am likely to take notice of the reading. So just noting the low, while not automatic, is pretty easy. Similarly the high pretty much always comes at a time when I can note it manually if I care to.
Since the OP said the list was of the things they "liked about" the acurite that they had, I didn't take that to mean they were a hard requirements. Something has to give somewhere if you are to capture high and low reading on the bike. At the very least you are likely to have false readings on the high end with anything that reads constantly. For me a good compromise is something that I can watch throughout the day and choose to read when it isn't prone to excessively high false readings.