In general, at least in my area, we do not have short term rentals in MLS. They ,mostly require a 12 months lease.
One good place to look for that is Craigslist. You might be able to find a 3 months lease, furnished.
You might also be able to ask Realtors and see if some of the owners might not mind renting their home out for a few months while the house is still on the market. Although for that, you will need to allow them of the convenience of showing the house and promise to keep the house in showing condition with short notice..