Anecdotal evidence time. AIO user.
At my location, for the last three days the ambient temperature as measured by a weather station has been in he range -5C to +5C, with the air temperature being above 0C for approx only 8 hours out of the 72 hours. MY AIO is outside, attached to the wall of my house, under over-hanging eaves but otherwise exposed to this chilly East Anglian weather. My standard usage pattern at this time of year is to fully charge and use mains power in the Octopus Go period of 00:30-04:30, then run down the battery to flat or close to flat, with flat often happening in the late evening. Solar charging has been strong for the Winter during this period - there has usually been a midday full top up. In addition, I manually topped up before and discharged during an Octopus Saving Session.
Over that 3 day period the battery temperature has been in the range 9.3C-22.6C, with the low points typically being just before the charging starts at 00:30. Relatively slow solar charging (3-4kW) only gives rise to a modest increase in battery temperature (a couple of degrees), but fast mains charging (6kW) gives a 10+C rise.
So there doesn't seem to be anything to worry about right now, as the combination of insulation and constant use seems to be keeping things at a pretty stable level. It'll be interesting to see how it behaves if we get an extremely cold and dark snap this winter. But I'm not rushing out to get the PIR just yet.