You live in the same part of the world as me
Yes, we (most on the forum) live in the same part of the world as you. The UK.
Remember the brood nest needs to be around 35 degrees Celsius, so the bees which have a compact nest, to keep the temperature controlled, will simply have to disperse a little more warm air, the first weapon in their 'air-con' arsenal. If they do not have enough nectar to evaporate (which requires an awful lot of thermal energy per unit mass), they would be bringing back water for extra evaporative cooling. So VM and drstitson have said enough to demonstrate there is no need for worrying on this score, and enrico has pointed out yet another benefit of an OMF.
Regards, RAB