3 factors here:
Thermal Shock (which affects fatigue life of the blade and ultimately leads to cracking due to thermal stresses generated). A blade will ultimately fail when cracks are created in the blade due to plastic hardening. Due to high cycle fatigue in turbines, the crack can propigate QUICKLY!
Creep (generated by temperature and centripetal forces on the blade, the first a function of load on the APU, the second a function of speed which is typically constant in APUs). Failure mode is Creep bursting or the tips wearing out the frangiable material leading to decrease in turbine efficiency and ultimately siezure.
At the end of the day, you have to do what your SOP/Local procedures specify! I would imagine the design point for apus are quite forgiving, as due to the nature of their operation. Many have centrifugal compressors, thus at least from the cold end, not too many worries. I would IMAGINE (not 100% on this) that the hot end would be designed more for longevity rather than fuel efficiency, meaning that the blade designer could get extra material in there to maximise vibration damping, whilst lower operating temperatures would minimise thermal stress cycles whilst perhaps not offering the best fuel efficiency.