Carlson (1983), p192 shows a pressure-temperature stability diagram for various polymorphs of CaCO3 however the scales are from 0 to 1200° C temperature and 0 to 40 kbar pressure.
The spelean environment is about 15° C and about 1 bar pressure only, which is in the stability range for calcite. At these temperatures and pressures, aragonite is unstable. Aragonite is stable above about 3 kbar pressure which does not occur in the surface environment.
Based on temperature and pressure alone, in the cave environment one would expect calcite to be the only form deposited yet aragonite does occur therefore there must be another factors other than temperature or pressure for aragonite to occur in caves.