T.N.
We built a house. Closed on our first house what we THOUGHT was 3 weeks before new house was done (tried to stretch it out as long as we could). We rented an apartment, put pretty much EVERYTHING in storage (A nightmare living in a two bedroom apartment with three kids and a dog and no stuff).
Three weeks turned into a month. A month turned into SIX MONTHS! ACK!
Maybe call a realtor and ask about REALLY short term rentals? They are out there.
Good Luck, I don't envy you!
:)