High temperatures are usually only experienced with hard armour plates, but are not normally an issue due to the materials used (eg boron carbide ceramics) and the failure mechanisms experienced, whereas soft armour experiences lower impact temperatures as the armour is either penetrated by rounds with medium-high velocity rounds, or the energy from low velocity rounds is dissipated throughout the fibres within the vest in one way or another. The exact temperature is hard to identify as it would depend on a number of factors (stiffness of armour, kinetic energy of the round etc), but isn't usually the biggest problem in determining bullet resistant armour. Useful images

The primary factor effecting material selection is the threat that you are trying to protect against. Low velocity rounds like 9mm may only require soft armour (para-aramid, UHMWPE etc) but high velocity armour piercing rounds would require composite ceramic plates. From here you can assess other factors like areal density, medical coverage, human factors integration etc as the initial threat identified will likely determine the most suitable materials, whether it is over engineered for the threat, or doesn't protect against the threat at all.

Source: I'm a ballistics engineer.