In this paper, a bio-heat transfer model of temperature distribution in human eye is discussed using appropriate boundary conditions for cornea and sclera. Variational finite element method with Crank-Nicolson scheme is used to calculate the transient temperature distribution in normal human eye. The temperature with and without the effect of blood perfusion and metabolism on retina is simulated and compared for various ambient temperatures, evaporation rates and lens thermal conductivities. The obtained results are compared with experimental results and past results found in literatures. The results show that the steady state corneal temperature is achieved in around 31 and 45 minute of exposure at ambient temperatures 10℃ and 50℃ respectively. Steady state eye temperature is achieved earlier at higher evaporation rate. Similar result is achieved for higher lens thermal conductivity and also for lower ambient temperature.