Microfluidic concentration is achieved using temperature gradient focusing (TGF) in a microchannel with a step change in cross-section. A mathematical model is developed to describe the complex TGF processes. The proposed mathematical model includes a set of governing equations for the applied electric potential, electroosmotic flow field, Joule heating induced temperature field, and sample analyte concentration distributions as well. Scaling analysis was conducted to estimate time scales so as to simplify the mathematical model. Numerical computations were performed to obtain the temperature, velocity and sample concentration distributions. Experiments were carried out to study the effects of applied voltage, buffer concentration, and channel size on sample concentration in the TGF processes. These effects were analyzed and summarized using a dimensionless Joule number that was introduced in this study. In addition, Joule number effect in the PDMS/PDMS microdevice was compared with the PDMS/Glass microdevice. A more than 450-fold concentration enhancement was obtained within 75 seconds in the PDMS/PDMS microdevice. Overall, the numerical simulations were found in a reasonable agreement with the experimental results.