From my personal past experience,
a rootbound fig tree will need watering in heat several times a day and thats not good.
Ever notice how water will sit on top for a while before it drains into the mix or run off to the side and right out the drain holes .
The water has a hard time penetrating into the soil if there are so many roots blocking it passage.
The bigger the plant and the smaller the pot without root work is not good such as some types that are vigorous growers and have been in a 3 gallon pot for 2 full growing seasons for it probably needed root pruning the past winter if its a good grower.
Slip plant out of pot and a rootbound plant will have roots all around it making contact with the inside of that pot just cooking and helping make the plant suffer in the heat of the day.
Potting up is fine in a pinch in my opinion but many wait till the roots are very full in orginal pot say a 1 gallon pot then slip out and put into a 3 gallon pot and add soil.
Thats fine for a full growing season, on a semi vigorous plant after a full growing season it will be at or near rootbound, the faster a plant grows so do its roots and when the 90 degree temps hit it probably will need a lot of watering.
It had been high 80s here recently, 90 yesterday 97 today and high 90s tomorrow my plants sit on landscaping rocks in full sun and some sit on cement patio in full sun. There doing well .
Some plants curl there leaves in sun no matter what like my Vdb , Pastilliere, Negretta - the pots are well hydrated and not root bound as i showed a forum member just yesterday that had stopped by and i said lift the pot its well watered which he did.
While others show little to no curl in the 90 plus heat like my hardy chicago, sals el.,dark port, ronde , jolly tiger.