A Dyson sphere is a hypothetical construct of a star purposely shrouded by a cloak of broken-up planetary material to better utilize all of the stellar energy. A clean Dyson sphere identification would give a significant signature for intelligence at work. A search for Dyson spheres has been carried out using the 250,000 source database of the IRAS infrared satellite which covered 96% of the sky. The search has used the Calgary database for the IRAS Low Resolution Spectrometer (LRS) to look for fits to blackbody spectra. Searches have been conducted for both pure (fully cloaked) and partial Dyson spheres in the blackbody temperature region 100 K ≤ T ≤ 600 K. When other stellar signatures that resemble a Dyson sphere are used to eliminate sources that mimic Dyson spheres very few candidates remain and even these are ambiguous. Upper limits are presented for both pure and partial Dyson spheres. The sensitivity of the LRS was enough to find Dyson spheres with the luminosity of the Sun out to 300 pc, a reach that encompasses a million solar-type stars.