The two-dimensional (2D) Galerkin vectorial finite-element method (FEM) with 2nd transparent boundary conditions (2nd TBC) is reported and the modes of fibers with arbitrary cross-section shape and arbitrary refractive indices distribution are analyzed. By 2nd TBC the confinement loss (CL) of modes of photonic crystal fibers (PCF) is solved more accurately than by 1st TBC. The relative error between results of FEM with 2nd TBC and multipode method (MM) is no more than 10%. After the temperature properties of a single mode PCF is numerically simulated, the approximate formulas for the change of effective refractive index neff, effective radius Reff and CL of PCF with temperature are constructed. When the temperature coefficient of refractive index ξ varies slowly within the range of wavelength and temperature, as temperature inceases, neff inceeases linearly and the increment has nothing to do with wavelength λ, diameter of air hole d and distance between two nearest holes Λ; Reff decreases linearly and the decrement is in proportion to ξ, temperature increment ΔT, Λ2 and λ2, and inverse proportion to d; CL decreases linearly and the decrement is in proportion to ξ, ΔT, and CL, CL varies more rapidly with larger d/Λ at a longer wavelength. The dispersive properties of PCF are not affected by temperature change.