Heat would definitely speed the process along if the wall is plaster.
There are so many ways to skin a cat, we have many options, turbo vents, Octidry, injectidry, Adaptidry & the Airwolf for structural drying.
We can also use the Intercepter HEPA with the Injectidry or the Adaptidry attached to airscrubber when the cavity has questionable microbial activity and they don't want to remove the materials.
If you get heat in the cavity and it will dry.
Be sure to do a thorough job of monitoring with penetrating meters to ensure dryness.