The influences of ion trapping and fluctuations of electron temperature and plasma flow on cross-beam energy transfer (CBET) are examined using two- and three-dimensional particle-in-cell simulations in parameter regimes relevant to recent CBET experiments at the OMEGA laser facility. In mid-Z plasma irradiated by an intense pump beam and weaker probe beam, ion trapping, collisional de-trapping, and plasma flow induced by thermal effects are shown to affect the CBET gain. Ion trapping can enhance or detune the CBET resonance [Nguyen et al., Phys. Plasmas 28, 082705 (2021)]. Collisional de-trapping can affect the CBET gain at low seed beam intensity near the onset threshold for ion trapping. Thermal-effects-induced flow can also detune the CBET resonance at a level comparable to that from trapping at low seed beam intensity. As a consequence, the CBET gain is sensitive to collisions and dimensionality at low seed beam intensity where ion trapping is weak but is insensitive to collisions and dimensionality at high seed beam intensity where ion trapping is strong.