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 3 years. Variability in the thermal infrared is identified using a combination of Spitzer's InfraRed Array Camera 3.6, 4.5, 5.8, and 8.0{mu}m bands, and the Multiband Imaging Photometer for Spitzer 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 ~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 (O-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. 59 variable stars from our list remain unclassified.