Compressor or Refrigerant dehumidifiers can not really reach below 45% Relative humidity.  A Desiccant or Absorption dehumidifier can reach to around 25% giving a lower vapor pressure to gradually dry.  There is always a degree of heat energy but more can be added.

Adding heat will excite the water molecules to the surface faster.  Some traditional lumber dryers for instance use compressor dehumidifiers and heating elements in order to get a lower relative humidity and therefore lower vapor pressure.

Using too much heat or drying too quickly, may mean the timber or a wall  becomes “case-hardened”.  The very outer skin becomes impervious to the flow of moisture through it.  In woods sometimes this can not be reversed.  In walls time to allow the plaster to “relax” may be needed simply by removing heat or dehumidification.

Vapor Pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system.