If they are adamant it is going to be done at that time, even if they are new piggies, then to be honest I would still bring them in anyway if there is a risk of smoke coming their way - their health would come before any settling in considerations
You will have to use a thermometer and see how things go - particularly if it isn’t a proper shed as such it may not trap heat in the same way.
A shed is a good idea and certainly for winter, a lot of us keep them in sheds but they can be tricky in summer.
A 15 degree consistently sunny day and my shed can easily reach well in excess of 20 degrees and of course if it gets too high then they have to come out into the run if I’m home or into the house if I’ve got to go out. I have internal mesh doors on my shed so I can leave the main doors open, close the mesh doors for ventilation and the boys are still safe, but that only works until certain temperatures.
There is a point that even having the internal doors doesn’t cool it enough. Mid summer for the last few years and my shed has hit 40 plus degrees consistently, not even cooling at night, so the boys move into the house for a few weeks as it’s usually even too hot in a hutch or even in the run outside. They then only go out early morning and late evening for run time
