The ion heating by voltage fluctuation noise in grooved planar ion trap is investigated. The direct method is used to calculate the ion heating and the length scale is obtained. The variation of length scale with ratio between width of groove and radio frequency electrode varied is calculated by using finite element method. And then the ion heating by resistance thermal fluctuation of control electrodes is also calculated by using fluctuation dissipation theorem. The spectral density of electric field fluctuation in x and y direction and better value of α are obtained.