  We present our study on the infrared variability of point sources in the
Small Magellanic Cloud (SMC). We use the data from the Spitzer Space Telescope
Legacy Program "Surveying the Agents of Galaxy Evolution in the Tidally
Stripped, Low Metallicity Small Magellanic Cloud" (SAGE-SMC) and the "Spitzer
Survey of the Small Magellanic Cloud" (S$^{3}$MC) survey, over three different
epochs, separated by several months to three years. Variability in the thermal
infrared is identified using a combination of Spitzer's IRAC 3.6, 4.5, 5.8, and
8.0 $\mu$m bands, and the MIPS 24 $\mu$m band. An error-weighted flux
difference between each pair of three epochs ("variability index") is used to
assess the variability of each source. A visual source inspection is used to
validate the photometry and image quality. Out of $\sim$2 million sources in
the SAGE-SMC catalog, 814 meet our variability criteria. We matched the list of
variable star candidates to the catalogs of SMC sources classified with other
methods, available in the literature. Carbon-rich Asymptotic Giant Branch (AGB)
stars make up the majority (61%) of our variable sources, with about a third of
all of our sources being classified as extreme AGB stars. We find a small, but
significant population of oxygen-rich AGB (8.6%), Red Supergiant (2.8%), and
Red Giant Branch (<1%) stars. Other matches to the literature include Cepheid
variable stars (8.6%), early-type stars (2.8%), young-stellar objects (5.8%),
and background galaxies (1.2%). We found a candidate OH maser star, SSTISAGE1C
J005212.88-730852.8, which is a variable O-rich AGB star, and would be the
first OH/IR star in the SMC, if confirmed. We measured the infrared variability
of a rare RV Tau variable (a post-AGB star) that has recently left the AGB
phase. Fifty nine variable stars from our list remain unclassified.
