We have used IRAS strip scans to study the infrared emission properties of 27 dominant galaxies that lie in the center of clusters rich in hot gas. In this sample, 30% of the objects were detected at 12/25 μm, while 46% were detected at 60/100 μm. The ratio of the infrared to optical flux densities is an order of magnitude greater than for elliptical and S0 galaxies. The presence of infrared emission is not obviously correlated with z, mv, Mv, the presence of young stellar populations, emission-line gas, the X-ray luminosity, or the cooling rate of hot gas M. The infrared luminosities, which are comparable to the X-ray and blue optical luminosities (1044-1045 ergs s-1), imply dust masses of 0.3-3 × 107 (Tdust/30 K)5.9 M⊙, and gas to dust ratios less than 1000 (Tdust/30 K)5.9. The dust grains are probably heated by collisions with electrons in the X-ray emitting gas, a process that also causes grain destruction. A possible supply of dust is stellar mass loss, although this may not be entirely adequate to balance the inferred destruction rate.