Vone Rotate,
You've quoted a CAS/Mach profile of 280 Kt / M0.76
For this speed schedule crossover will occur at Pressure Height of 31189.1 ft, where the Equivalent Airspeed (EAS/Ve) will be 266.7 Kt, and the Static Pressure 284.96 hPa / 8.415"Hg.
Temperature will be..............Who cares? Temperature is not a factor.
Density Height will be............Who cares? Density Height is not a factor.
For a 280 Kt / M0.76 speed schedule, crossover height will be the same EVERY time, regardless of temperature. Different speed schedules have different crossover heights, for example a speed schedule of 280 Kt / M0.78 will always occur at 32473 ft.
TEMPERATURE AND DENSITY IS NOT A FACTOR!
Regards,
Old Smokey