We demonstrate a method of concentrating and patterning of biological cells on a chip, exploiting the confluence of electric and thermal fields, without necessitating the use of any external heating or illuminating sources. The technique simply employs two parallel plate electrodes and an insulating layer over the bottom electrode, with a drilled insulating layer for inducing localized variations in the thermal field. A strong induced electric field, in the process, penetrates through the narrow hole and generates highly nonuniform heating, which in turn, results in gradients in electrical properties and induces mobile charges to impose directional fluid flow. The toroidal vortices, induced by secondary electrokinetic forces originating out of temperature-dependent electrical property variations, transport the suspended cells toward a hot-spot site of the chip, for rapid concentrating and patterning into different shaped clusters based on predesigned conditions, without exceeding safe temperature limits that do not result in damage of thermally labile biological samples. We characterize the efficacy of the cell trapping process for two different biological entities, namely, Escherichia coli bacteria and yeast cells. These results have importance toward developing biomedical microdevices for drug discovery, antibiotic resistance assessment, and medical diagnostics.