you could use collision theory to answer this. The immobilised enzyme is immobilised i.e. it can't move this means that this immobilisation will limit the amount of collisions that can occur between the substrate and the active site of the enzyme. Less collisions means less products in the given time, therefore rate will be slower if immobilised than if it is free.
If the enzyme is immobilised is a substance such as sodium alginate you could talk about diffusion distance. In the immobilised enzyme, the enzyme is surrounded by the alginate to form a bead. It will take time for the substrate to diffuse through the alginate and reach the enzyme therefore the rate of the retain of the immobilised enzyme (relative to the free enzyme) is slower.
All this is provided that the temperature isn't high enough to denature the free enzyme so even if the temperature is constant you've got to make sure it isn't too high in the first place to cause denaturation.