A numerical investigation is conducted on the electroosmotic flow and associated heat transfer in a two-dimensional microchannel. The objective of this study is to explore a new conceptual idea that is control of an electroosmotic flow by using a thermal field effect through the temperature-dependent physical properties. Two exemplary problems are examined: a flow in a microchannel with a constant vertical temperature difference between two horizontal walls and a flow in a microchannel with the wall temperatures varying horizontally in a sinusoidal manner. The results of numerical computations showed that a proper control of thermal field may be a viable means to manipulate various non-plug-like flow patterns. A constant vertical temperature difference across the channel produces a shear flow. The horizontally-varying thermal condition results in spatial variation of physical properties to generate fluctuating flow patterns. The temperature variation at the wall with alternating vertical temperature gradient induces a wavy flow.