The record-breaking high temperatures over the past few days provided great validation that good insulation and decent air tightness keep heat out in summer as well as keeping heat in in winter.
Any house is going to heat up a bit, through a combination of heat transfer from the outside as well as internal gains from appliances and occupants. The biggest risk is a huge amount of solar gain through windows but by keeping blinds closed (and windows closed, obviously) that can be minimised.
With such high temperatures being forecast I took the precaution of slightly over-cooling by opening some windows overnight beforehand, and then opening at night whenever the outside temperature was lower than the inside (which was not until about 04:30 on the morning of the 19th).
The master bedroom stayed below 25 degrees at all times; I’m happy with that.