Abstract Thermal radiation is found from a moving point charge along a special, globally defined, continuous accelerated trajectory. The calculation is entirely classical (despite the appearance of ℏ) but is shown to have an immediate connection to quantum field theory via the moving mirror model. A precise recipe is given for the functional mathematical identity of the electron–mirror duality that allows one to map between (1) the classical radiation of an ordinary accelerating point charge in 3+1 Minkowski spacetime and (2) the quantum radiation of a moving mirror in 1+1 flat spacetime, for a given rectilinear trajectory.