Yes, and not all spherical's are alike either. CCI changed their magnum primer formulation in 1989 to accommodate the needs of the military WC8## series of St. Marks powders. Talking with a Western Powders tech, I learned the coatings on newer offerings like the Ramshot line have more modern coating chemistry that doesn't need the warmer primer for best ignition consistency and they have more temperature stabilization. So you really can't generalize too much about this. Also, Denton Bramwell showed barrel temperature mattering more than powder temperature in tests here
The stability really does change with starting pressure and peak pressure. Hence the case fill effect. The best common example (I think maybe Denton mentions it) is Varget doing very well about apparent temperature stability in the .308, but being no better or worse than a number of other powders when used in the .223. When you think about it, because rate of change in pressure is determined by the powder progressivity curve interacting with the rate of expansion, chamberings that have different expansion ratios and different average velocities will not be needing the same temperature compensation. So there's really no one-size-fits-all temperature compensation scheme.
Hodgdon's comparative data
for some powders in their Extreme line that Mahevey posted isn't all fired in the same cartridge with the same average muzzle velocity. If you take the variations as a percentage of average muzzle velocity for the individual cartridges, the worst/best thing can change order.