Installation of a flow inducer shroud

I have a 6" well hole with an inside diameter of 5". My pump is 4" and may be set below the bottom of the casing. I don't know how deep the casing goes. The well is 115' deep and water level is about 45' down. With the low producing well, about 3 - 4 gal per minute, I think I want the pump at 105'. With this configuration I have read that I need a skirt, also called a flow inducer shroud around the intake and motor to keep the motor cool. It is just a 1/2 hp 220 v 2 wire pump motor. I don't think there is enough room to put a big enough skirt down the 5" hole. If the pump motor is under water, I would think it would be cool enough anyway. Would this be correct? Thanks for you comments, Henry