No one has mentioned this (unless I missed it) but having the entire cage (all sides) wrapped in foil seems a bad idea -- CHE or not. That is too much coverage that doesn't allow for airflow or for light.
I think it would be best to only have that foil on 3 sides. Allow the front to be open for airflow and light.
Getting that thermostat will be critical. It will be much work for you to keep the temp regulated without it. It won't be a fun month and it won't be ideal for your hedgehog which will doubtless be getting lots of temp fluctuations until the thermostat is set up.
here with my Mecki-- born 2/12/19