It is a good idea
A shoebox house maybe - can be permanent as well as temporary! Using the lid for a lift-off roof. There aren't that many houses with lift-off roofs and getting the size right for the hamster and to fit the cage can be tricky.
If she is using a corner of the cage for her toilet, this house is probably a good size for nesting and hoarding. The Ferplast Sin range are sort of flatpack and fit together like a jigsaw. The guinea pig size one is far too small for a guinea pig and about the right size for a hamster. If it's a bit tall to fit under the shelf you can just push it down into the substrate a bit. I had the rabbit sized one for a while but that is massive!
https://www.amazon.co.uk/Ferplast-Gu...inea+pig+house
Rodipet make really good houses with lift-off roofs but they are a bit expensive - the postage is about £8. Which isn't too bad if you're buying other things from them at the same time, because it's a flat rate of £7 to £8 whether you get one item or a large parcel. But it adds to the cost of the house quite a bit and they average about £16 in price after converting into pounds. The ones with the granite tops are quite good because it's also something to help keep nails short (it's rough granite) - but I just bought the square of granite separately and had it on the shelf under the water bottle.
The two room Dalani one is popular in these. The three room is good two but might be a bit big for the cage.
https://www.rodipet.de/shop/haeuser/rodipet-granit/
They also do ones that fit together like a jigsaw like the Ferplast sin. The two room one on here is good as well - it's slightly longer than the Ferplast sin house.
https://www.rodipet.de/shop/haeuser/...s-stecksystem/