A thorough numerical investigation of the two-dimensional heat transfer and laminar flow around a single circular cylinder was performed. The main interest of this study was the flow configuration of a heated cylinder in the vicinity of a wall under conditions that resemble the flow past a hot-wire anemometry (HWA) probe. A finite volume Navier-Stokes solver enhanced by local block refinement and multigrid acceleration guaranteed highly accurate and efficient computational results. As a reference for the influence of the Reynolds and Prandtl numbers on the drag coefficient C(D) and Nusselt number Nu, the limiting case of a cylinder in free stream with a very small temperature loading (T = 1.003) was analyzed first. Calculations were performed in the Re range 10-4 to 102. All the results agreed well with available analytical/numerical and experimental results. By comparison with the reference results, the influence of the temperature dependence of the fluid properties on C(D) and Nu was determined. After these extensive verification predictions a study on the influence of the wall proximity in near-wall HWA measurements was tackled based on two limiting cases, a highly conducting and an insulating wall. The investigation allowed an estimate of the velocity correction needed by HWA data. The results for a highly conducting wall agreed well with available experimental results. A new form of bounded velocity correction was proposed for this case. The results for the case of an insulating wall were unexpected and contradictory to previous experimental observations. A detailed analysis of the numerical solution revealed new aspects of this complex flow situation. Existing experimental results with 'nonconducting' wall materials were shown to reflect a combination of the extreme situations computed numerically.