We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection in a square cavity by direct numerical simulations.The Rayleigh number range is 1 × 108 ≤ Ra ≤ 1 × 1013,and the Prandtl number is selected as Pr =0.7 and Pr =4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuation θrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max ～ (z/δ)0.99±0.01,where z/δ is a dimensionless distance to the boundary (δ is the thickness of thermal boundary layer).Out of the boundary layer,when Ra ≤ 5 × 109,the profiles of θrms/θrms,max descend,then ascend,and finally drop dramatically as z/δ increases.While for Ra ≥ 1 × 1010,the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation V has a power law dependence on Ra,given byV～Ra-0.14±0.01.