  We propose a practical scheme for one-way quantum computing based on
efficient generation of 2D cluster state in thermal cavities. We achieve a
controlled-phase gate that is neither sensitive to cavity decay nor to thermal
field by adding a strong classical field to the two-level atoms. We show that a
2D cluster state can be generated directly by making every two atoms collide in
an array of cavities, with numerically calculated parameters and appropriate
operation sequence that can be easily achieved in practical Cavity QED
experiments. Based on a generated cluster state in Box$^{(4)}$ configuration,
we then implement Grover's search algorithm for four database elements in a
very simple way as an example of one-way quantum computing.
