The intriguing connection between Black holes' evaporation and the physics of solitons is opening novel roads to finding observable phenomena. In particular, due to the recent observation of gravitational waves, Hawking radiation of moving black holes is one of the first candidates to investigate. However, a theoretical context for the description of this phenomenon is still lacking. Here, we adopt a soliton geometrization technique to study the quantum emission of moving black holes in a one-dimensional model. Representing a black hole by the one soliton solution of sine-Gordon equation, we consider Hawking emission spectra of quantized massless scalar fields on the soliton-induced metric. We study the relation between the soliton velocity and the black hole temperature. Our results address a new scenario in the detection of new physics in the quantum gravity panorama.