  We show that null surfaces defined by the outgoing and infalling wave fronts
emanating from and arriving at a sphere in Minkowski spacetime have
thermodynamical properties that are in strict formal correspondence with those
of black hole horizons in curved spacetimes. Such null surfaces, made of pieces
of light cones, are bifurcate conformal Killing horizons for suitable
conformally stationary observers. They can be extremal and non-extremal
depending on the radius of the shining sphere. Such conformal Killing horizons
have a constant light cone (conformal) temperature, given by the standard
expression in terms of the generalisation of surface gravity for conformal
Killing horizons. Exchanges of conformally invariant energy across the horizon
are described by a first law where entropy changes are given by $1/(4\ell_p^2)$
of the changes of a geometric quantity with the meaning of horizon area in a
suitable conformal frame. These conformal horizons satisfy the zeroth to the
third laws of thermodynamics in an appropriate way. In the extremal case they
become light cones associated with a single event; these have vanishing
temperature as well as vanishing entropy.
