We present and analyze 58 transit light curves of TrES-3b and 98 transit light curves of Qatar-1b, observed by the Transiting Exoplanet Survey Satellite, plus two transit light curves of Qatar-1b, observed by us, using a ground-based 1.23 m telescope. These light curves are combined with the best-quality light curves taken from the Exoplanet Transit Database and the literature. The precisely determined midtransit times from these light curves enable us to obtain the refined orbital ephemerides, with improved precision, for both hot Jupiters. From the timing analysis, we find indications of the presence of transit timing variations (TTVs) in both systems. Since the observed TTVs are unlikely to be short-term and periodic, the possibility of additional planets in orbits close to TrES-3b and Qatar-1b is ruled out. The possible causes of long-term TTVs, such as orbital decay, apsidal precession, the Applegate mechanism, and line-of-sight acceleration, are also examined. However, none of these possibilities are found to explain the observed TTV of TrES-3b. In contrast to this, line-of-sight acceleration appears to be a plausible explanation for the observed TTV of Qatar-1b. In order to confirm these findings, further high-precision transit and radial velocity observations of both systems would be worthwhile.