I just have a simple answer for this.
Rate of effusion is the rate at which a gas is allowed to escape from a given cross sectional area(orifice) due to pressure difference.
While diffusion is the tendency of gases to mix with each other spontaneously and form a homogeneous mixture.
In case of diffusion, increasing temperature increases the rate of diffusion because it increases the kinetic energy of molecules which increases the mixing ability of the gases and thus, diffusion.
In effusion the same thing happens, kinetic energy of molecules increases, which increases the speed of the molecules. But Increase in speed of the molecules decreases the probability of the molecules to escape through the given orifice/hole in a given time.
Therefore, rate of effusion decreases with increase in temperature.