Dear Jimmys Mum,
I performed an artificial swarm on my strongest colony in late April and decided to try using a Snelgrove Board for the first time. When I inspected the relevant brood box on 2 May, a virgin queen had emerged from its cell. I then refrained from looking again until today (12 May) when I found eggs in about 10 cells, all in a row at the bottom of a frame. There was a single egg in all but one of these cells, and that one contained three eggs at the centre of the cell floor. All the bees were astonishingly well behaved. I assume that I have a recently-mated queen in there and that she might even have started laying eggs for the very first time today. Presumably, she inadvertently released more than one egg on one of these occasions, which I understand can happen when queens have only recently started laying. (Had I shaken the frames a bit harder, it is possible that I might have found more eggs but I saw no real need to do so).
The maximum daily temperatures recorded at a reasonably local weather station, in degrees Celcius from 2 May until today, were 13, 18, 15, 14, 13, 15, 15, 16, 15, 19 and 15 (Source: wunderground.com) . Mean daily temperatures over the same timeframe were 8, 14, 12, 12, 10, 10, 10, 12, 11, 14 and 12. It would seem that this provided sufficient opportunity for successful mating flights. Various caveats apply regarding those actual readings and further caveats apply with regard to their application to my newly-mated queen. However, if several of us collected the equivalent data each time we performed an artificial swarm, within a year or two we might be able to provide a reasonably validated “rough and ready” forum-generated answer to your original question.
Hope all goes well with your six virgin queens!