An approximate analysis is presented for the prediction of the over-all average heat-transfer coefficients from spheres to air in the transition-flow region, that region wherein the mean free molecular path is small but not negligible when compared with the sphere diameter. The analysis is made on the basis of a simplified flow field and the utilization of the continuum formulation of the energy equation with the rarefaction effects being accounted for entirely in the boundary conditions. The results of the analysis are compared with experimental heat-transfer data from spheres to air in the transition-flow region, with heat-transfer data from spheres to air in the continuum-flow region, and with the calculated results of heat transfer from spheres in the free molecule-flow region. Experimental free-stream recovery factors are presented for spheres. Significant flow parameters and flow-region limits for the transition region are discussed.