In response to your question, as it applies to black and white processing of negatives designed for enlargement, the determiner of the proper time/temperature correlation would be the density of the highlights in the negative. This would ultimately determine whether the negative would print with a full tonal range. (This assumes that the photographer is exposing the scene to gain adequate shadow detail and is cognizant of the desired development of the negative).
Typically, the contrast range of a properly exposed and developed negative would be on the order of 1.20-1.30 (above FB+fog) for a negative designed for enlarging with a diffuse light source and on the order of 1.10-1.20 (above FB+fog) for a negative designed for enlarging with a condensor or point light source. The means by which one reaches that density contrast range by whatever variable of time and temperature is immaterial.