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In this paper, blackbody radiation (BBR) temperature rise seen by the$^{40}$Ca$^+$ ion confined in a miniature Paul trap and its uncertainty havebeen evaluated via finite-element method (FEM) modelling. The FEM model wasvalidated by comparing with thermal camera measurements, which were calibratedby PT1000 resistance thermometer, at several points on a dummy trap. The inputmodelling parameters were analyzed carefully in detail, and their contributionsto the uncertainty of environment temperature were evaluated on the validatedFEM model. The result shows that the temperature rise seen by $^{40}$Ca$^+$ ionis 1.72 K with an uncertainty of 0.46 K. It results in a contribution of 2.2mHz to the systematic uncertainty of $^{40}$Ca$^+$ ion optical clock,corresponding to a fractional uncertainty 5.4$\times$10$^{-18}$. This is muchsmaller than the uncertainty caused by the BBR shift coefficient, which isevaluated to be 4.8 mHz and at 10$^{-17}$ level in fractional frequency units.

Evaluation of blackbody radiation shift with temperature associated fractional uncertainty at 10E-18 level for 40Ca+ ion optical clock