GPS height is, as a rule of thumb, up to three times less accurate than GPS horizontal position. The GPS horizontal position is typically less then 10 meters off, vertically it's typically accurate to about 30 meters or 100 ft.
Of course there are times that exceptional bad geometries of the GPS satellites cause outliers. The factor 3 is only a rule of thumb, not a guarantee.
To observe this at the stand is not a good idea. At the ground, especially in between buildings / tailplanes, the GPS signals are reflected and reach your GPS antenna via multiple paths. Hence the accuracy at the stand is not comparable to in-flight accuracy. During taxiing it is in general good.
To compare GPS height to barometric (QNH) altitude is a bit tricky. You already mentioned the temperature correction, which is an important factor. However, for obstacle clearance it could be beneficial to use GPS since you don't need to correct for temperature in that case.
Another important factor is the fact that GPS uses the WGS84 ellipsoid as height datum internally, while we are used to measuring height with respect to Mean Sea Level. The difference between the two varies depending on your location on the earth but be as much as +/- 100m. / 300ft. Europe is for example about 100 to 250 feet above the reference ellipsoid, the US is 20 to 100 feet below. This difference is accurately modeled by
EGM96. Since that model is quite complex and requires heavy calculations a much simpler and slightly less accurate model is usually used inside avionics systems to convert for Height Above Ellipse (HAE) to MSL and vice versa.
The GPS height display in the cockpit may either show HAE or MSL. Only if MSL is displayed it could be suitable for obstacle clearance.
But please use the altimeter and correct that for temperature. Only use GPS height as a backup.
Best regards,
ATCast
See also:
Altimeter altitude vs GPS altitude
GPS altitude