  We present a set of {\it Spitzer} 24$\mu$m MIPS time series observations of
the M-dwarf eclipsing binary star GU Bo\"otis. Our data cover three secondary
eclipses of the system: two consecutive events and an additional eclipse six
weeks later. The study's main purpose is the long wavelength (and thus limb
darkening-independent) characterization of GU Boo's light curve, allowing for
independent verification of the results of previous optical studies. Our
results confirm previously obtained system parameters. We further compare GU
Boo's measured 24$\mu$m flux density to the value predicted by spectral fitting
and find no evidence for circumstellar dust. In addition to GU Boo, we
characterize (and show examples of) light curves of other objects in the field
of view. Analysis of these light curves serves to characterize the photometric
stability and repeatability of {\it Spitzer's} MIPS 24\micron array over short
(days) and long (weeks) timescales at flux densities between approximately
300--2,000$\mu$Jy. We find that the light curve root mean square about the
median level falls into the 1--4% range for flux densities higher than 1mJy.
Finally, we comment on the fluctuations of the 24\micron background on short
and long timescales.
