Streak cameras applied to inertial confinement fusion research and flashless imaging lidar require large working areas. However, the larger the working area, the bigger the temporal distortion is. And the temporal distortion has a great influence on the detecting precision of the streak camera, resulting in an image distortion on the screen. Yet previous streak camera design work emphasized shorter time resolution and higher special resolution with paying less attention to the temporal distortion extent. Key factors that may affect the temporal distortion are thoroughly analyzed in this paper. We calculate the electric field of a small-size streak tube with the aid of the Computer Simulation Technology Particle Studio software which is a three-dimensional electromagnetic simulation software based on finite integration technology. Axial electric field distributions at different distances to the axis of the small-size streak tube are displayed. The electron trajectories launched from different points on photocathode of the streak tube are tracked through interpolating pre-calculated electromagnetic field to the particle position. It is known that curved photocathode can reduce the temporal distortion, so we calculate the temporal distortions of streak tubes whose radii of curvature of the photocathode are 30 mm, 35 mm, 40 mm, 45 mm, 50 mm, and 55 mm respectively to ascertain how the curvature influences the temporal distortion. The results show that the temporal distortion is mainly produced in the photocathode-to-deflector region, and it is negligible in the equipotential region. Also, bigger radius of curvature of the photocathode leads to a positive temporal distortion, and smaller one leads to a negative temporal distortion. And the absolute value of the temporal distortion increases with the increase of the slit length. The small-size streak tube whose radius of curvature of the photocathode is 40 mm owns the smallest temporal distortion. We also calculate the temporal distortions of electrons launched from the different positions of the photocathode with different initial energies, and the initial energy has little influence on the temporal distortion. To sum up, the dominating factor that produces the temporal distortion is the curvature of the photocathode. The slit image under a ramp sweeping voltage on screen is curved due to the temporal distortion. And the bigger the temporal distortion, the greater the curvature of the slit image is. Besides, a linear relation between the temporal distortion and deflection of the slit image is displayed. The spatial resolutions of the streak tubes with the radii of curvature of the photocathode 30 mm, 40 mm, 50 mm are calculated respectively. And the small-size streak tube whose radius of curvature of the photocathode is 30 mm has the highest spatial resolution. The radius of curvature of the streak tube photocathode should be carefully selected according to actual requirements for the streak camera. Through the analysis we provide a significant guidance for streak tube design.