I used two solo cups, with one inserted into another. If you follow my lead, make three strips instead of two. If the cardboard is poor quality, it can get soft and tear. Mine did. The idea of using two cups like this is that you can slide the inner cup out of the outer one and put it into the final container w/o a slightest stress.
If you wonder what this thing is inside the plastic bag, it's dried seaweed that I found on the beach. I use it for isolation - so that the solo cup doesn't get hot during the day and doesn't cool down too much during the night. I kept my seedling on the balcony from day one. Both the day and night temperatures were almost comfortable for that.