  We give a simple differential geometric proof of the conformal transformation
of the night sky under change of observer. The proof does not rely on the four
dimensionality of spacetime or on spinor methods. Furthermore, it really shows
that the result does not depend on Lorentz transformations. This approach, by
giving a transparent covariant expression to the conformal factor, shows that
in most situations it is possible to define a thermal sky metric independent of
the observer.
