We present results from Spitzer Space Telescope observations of the mid-infrared phase variations of three short-period extrasolar planetary systems : HD 209458 , HD 179949 and 51 Peg . We gathered Infrared Array Camera ( IRAC ) images in multiple wavebands ( 3.6 \mu m or 4.5 \mu m , and 8 \mu m ) at eight phases of each planet ’ s orbit . We find the uncertainty in relative photometry from one epoch to the next to be significantly larger than the photon counting error at 3.6 \mu m and 4.5 \mu m. We are able to place 2 \sigma upper limits of only \sim 2 % on the phase variations at these wavelengths . At 8 \mu m the epoch-to-epoch systematic uncertainty is comparable to the photon counting noise and we detect a phase function for HD 179949 which is in phase with the planet ’ s orbit and with a relative peak-to-trough amplitude of 0.00141 ( 33 ) . Assuming that HD 179949b has a radius R _ { J } < R _ { p } < 1.2 R _ { J } , it must recirculate less than 21 % of incident stellar energy to its night side at the 1 \sigma level ( less than 26 % at the 2 \sigma level , where 50 % signifies full recirculation ) . If the planet has a small Bond albedo , it must have a mass less than 2.4 M _ { J } ( 1 \sigma ) . We do not detect phase variations for the other two systems but we do place the following 2 \sigma upper limits : 0.0007 for 51 Peg , and 0.0015 for HD 209458 . Due to its edge-on configuration , the upper limit for HD 209458 translates , with appropriate assumptions about Bond albedo , into a lower limit on the recirculation occuring in the planet ’ s atmosphere . HD 209458b must recirculate at least 32 % of incident stellar energy to its night side , at the 1 \sigma level ( at least 16 % at the 2 \sigma level ) , which is consistent with other constraints on recirculation from the depth of secondary eclipse depth at 8 \mu m and the low optical albedo . These data indicate that different Hot Jupiter planets may experience different recirculation efficiencies .