We present new Spitzer observations of the phase variation of the hot Jupiter HD 189733b in the MIPS 24 micron bandpass, spanning the same part of the planets orbit as our previous observations in the IRAC 8 micron bandpass (Knutson et al. 2007). We find that the minimum hemisphere-averaged flux from the planet in this bandpass is 76 +/- 3% of the maximum flux; this corresponds to minimum and maximum hemisphere-averaged brightness temperatures of 984 +/- 48 K and 1220 +/- 47 K, respectively. The planet reaches its maximum flux at an orbital phase of 0.396 +/- 0.022, corresponding to a hot region shifted 20-30 degrees east of the substellar point. Because tidally locked hot Jupiters would have enormous day-night temperature differences in the absence of winds, the small amplitude of the observed phase variation indicates that the planets atmosphere efficiently transports thermal energy from the day side to the night side at the 24 micron photosphere, leading to modest day-night temperature differences. The similarities between the 8 and 24 micron phase curves for HD 189733b lead us to conclude that the circulation on this planet behaves in a fundamentally similar fashion across the range of pressures sensed by these two wavelengths. One-dimensional radiative transfer models indicate that the 8 micron band should probe pressures 2-3 times greater than at 24 micron, although the uncertain methane abundance complicates the interpretation. If these two bandpasses do probe different pressures, it would indicate that the temperature varies only weakly between the two sensed depths, and hence that the atmosphere is not convective at these altitudes. (abridged)