We did this when we couldn't find anything to buy but needed to sell to relocate for the start of a new school year. Rental wasn't really an option after researching it, all letting agents told us we'd have no chance getting a rental as there was so much competition from long term tenants and so few properties available that a landlord would never pick us out of the 10-15 applications they get for every property. We could have rented something in another town 20 mins drive away but it wasn't a nice area and I thought it would be unsettling being so far from our school place, plus hard to manage around our working hours. So be very careful to check if renting is a realistic option for you before agreeing to move out.
We contacted a few Air BNB and independent holiday cottages and as we were moving over the autumn/winter reason a couple were willing to negotiate a longer term let rate, but some had bookings months ahead so we would have had the uncertainty of moving out then back in again for those weekends. Plus the rent was going to be a lot higher than a long term rental or mortgage (£2K a month instead of roughly £900 for a normal private landlord rental in our area). Fine for a month or two, but as it happened we ended up living with family for nearly a year as our property search took much longer than we expected and a purchase fell through.
We were very fortunate to be able to move in with family to save money and be in the location we wanted, but it did strain relationships so again something to really consider how long you might be able to stay for and a back up plan if things take longer than expected. Without children I think you could manage, but we found it really hard as it was squeeze, plus the children found it upsetting having so many of their toys and belongings in storage as there wasn't room for it all at our relatives house. If we had rented we wouldn't have needed to put much in storage.
Things worked out for us in the end as we saved money and could hold out for the perfect property, but but we were overly optimistic how long things would take, and the impact on how well the children settled was greater than I expected as on top of missing their friends and adjusting to a new school they didn't have the security of a home and their familiar belongings around them.
Sorry that's an essay, but hope our experiences give you something to reflect on