Most moves can be made from one home to the next without the need for temporary housing. In some cases the timing just doesn't work out , so it will become necessary to locate a "short term rental."
Defining "short term rental" is important. Usually the term is less than 30 days, but could be much longer if you purchasing a newly built home.
Your options are to either use an "extended stay" or a "corporate housing arrangement. The difference is usually price, with Corporate Housing being more expensive.
Extended stay choices are offered by many hotels. The rates are sometimes negotiable and get better after you have stayed longer than 30 days. These hotels cater to short term guests, by offering small suites with a living room and kitchen facilities. Many provide a nice, self serve breakfast and other homey amenities as laundry, exercise rooms, Internet access, local phone and fax service.
Corporate Housing choices offer a wider variety of housing. Corporate Housing can be anything from a modest apartment to a luxury estate. You will find Corporate housing via a property manager or possibly a private party ad in the newspaper.
Another option is to rent a furnished apartment. This option is obviously necessary if you needing a place on the longer side of short term! It is a more expensive option. Either you, or the complex will rent whatever furniture you need, so you don't have to disturb your personal belongings.
Where to look...
Local Newspapers
Property Managers
Online Sources
Extended Stay