A hot spot model for superconducting hot electron bolometers is presented based on a two-dimensional heat transport equation for electrons and phonons including heat trapping due to quasiparticle bandgap gradients. Skin effect concentrates the RF heating in lateral regions of the bridge and the bias current in the center. A reduction in conversion gain compared to a one-dimensional hot spot model is explained by the RF and bias heating profiles not being identical. An experimentally verified increase of the IF bandwidth from 3.5 GHz to 8 GHz when increasing bias voltage is predicted. IV curves, gain and noise are in very good agreement with measurements.