Don't, if you can help it. A cool closet in your flat would be better.
If that isn't an option, coolest driest you can get. Under a table (shade) in contact with the ground in a bin with a tight lid and some kind of desiccant to keep it dry. You could use silica gel (like fancy kitty litter or for drying flowers), damp-rid (which is actually an icemelt and fertilizer), or plain dry white rice or salt. Something to keep them from molding or sprouting.
"You must be the change you want to see in the world." "First they ignore you, then they laugh at you, then they fight you, then you win." --Mahatma Gandhi
"Preach the Gospel always, and if necessary, use words." --Francis of Assisi.
"Family farms work when the whole family works the farm." -- Adam Klaus
We store our dry saved and bought seed in glass lidded jars labeled with the contents...and then in the dark and always the coolest spot in the house. I would worry that a poly tunnel would get too hot, too damp, etc. but if that is absolutely your only choice I suppose seeds in jars and then a sealed white bucket on the ground might work for a few seasons. I do keep a lidded bucket of buckwheat for cover cropping in my garden shed with no problem but my more special seeds get pampered.
"We're all just walking each other home." -Ram Dass
"Be a lamp, or a lifeboat, or a ladder."-Rumi
“When it is understood that one loses joy and happiness in the attempt to possess them, the essence of natural farming will be realized. The ultimate goal of farming is not the growing of crops, but the cultivation and perfection of human beings.”
― Masanobu Fukuoka, The One-Straw Revolution