And I'm just in the final stages of preparing a compromise between Brian's & Graham's ideas, plus a few other ideas...

My new design is essentially a block of expanded polystyrene, with a blackened foil disk (with OS temp probe sensor just poking through), wrapped in cling film, and fitted into a pipe which is then also wrapped in cling film. There is a bit more to it that, but those are the headlines.
I've been taking pictures as I go and hope to be providing more detail later, perhaps next weekend. Attached is a picture showing it in a late stage of construction.
The new design has now spent 2 days/nights outside, but it is not in the final location yet because I need a pipe bracket from the builders' merchant and I am unlikely to get there before Friday. That means it is currently on the opposite side of the house to the main outdoor sensor, which given the apparent sensitivity means I don't think I can reasonably calibrate it yet (i.e. it needs to be much closer to the main outdoor sensor) - but I've already seen a night time difference of nearly 4 oC (4 times the difference in my glass jar at the same time) and we've not had anything close to a clear sky.
Interestingly I'm not seeing vastly higher day time differences in the new sensor than in the glass jar. I suspect that this is because the cling film is allowing heat to escape more easily than the glass does - but as I said I think I need all the sensors (main outdoor, old glass temp in a jar and new) close together before I can produce good data for analysis.
As an indication, the attached graph shows the first 24hrs, comparing main outdoor, old glass temp in a jar and new. It was a pretty overcast day, followed by an overcast (raining lightly for much of it) night. Particularly interesting (a subject for further study) is the bit just after 2000 at which point it started to rain. The jar temp fell markedly at the point but the 'double glazed' new sensor was more steady. My assumption is that this was due to the cooling effect of rain on the glass jar - it was to combat that effect that I built 'double glazing' into the new sensor.