A poorly insulated house would heat up quicker, and so have a higher peak indoor temperature. They will lose heat faster at night, yes, but if you ran a comparison with each house starting at the same temperature and allowing them both to equalise at the end, the average temperature of both would be the same.

The key insight is that insulation makes it slower for the outside temperature to heat the house up as well as to cool it down, so in a heatwave, insulation blunts the worst of it. Also you can actively reduce the insulative properties of a house by opening all the windows, so that it actually cools down much faster at night. This means that, in practice, the average temperature of the well-insulated house will be lower than that of the poorly one.

This kind of conversation (which occurs repeatedly whenever the weather gets hot in the UK) makes me despair, because we all need to be insulating our houses better, both to reduce our energy usage in the winter, and to protect against extreme heat.

"The situation is bad, therefore this makes no difference"

Am I reading this right?

I'd keep things battened down so you're starting from a lower base.

A breeze can be provided by a fan. (And it makes a huge difference - bigger than the breeze through a window)