Through the serendipitous discovery of infrared echoes around the Cas A supernova remnant, the Spitzer satellite has provided astronomers with a unique opportunity to study the properties of the echoing material and the history and nature of the outburst that generated these echoes. In retrospect, we find that the echoes are also clearly visible as infrared "hot spots" in IRAS images of the region. The spectra of the echoes are distinct from that of the dust in the general diffuse interstellar medium (ISM), revealing hot silicate grains that are either stochastically heated to temperatures in excess of ~150 K or radiating at an equilibrium temperature of this value. We show that the maximum luminosity that can be generated by the radioactive decay of ⁵⁶Ni is not capable of producing such spectra, and could therefore not have given rise to the echoes. Instead, we find that the echoes must have been generated by an intense and short burst of EUV-UV radiation associated with the breakout of the shock through the surface of the exploding star. The inferred luminosity of the burst depends on the amount of attenuation in the intervening medium to the clouds, and we derive a burst luminosity of ~1.5 × 10¹¹ L for an assumed H-column density of 1.5 × 10¹⁹ cm⁻². The average H-column density of the IR-emitting region in the echoing clouds is about 5 × 10¹⁷ cm⁻². Derivation of their density requires knowledge of the width of the echo that is sweeping through the ISM, which in turn is determined by the duration of the burst. A burst time of ~1 day gives a cloud density of ~400 cm⁻³, typical of dense IR cirrus.