does your blower get hot

The positive displacement blowers are especially bad about heat soaking. They generally sit right on top of the engine valley, collecting the heat rising off the engine. The intercooler systems for PD blowers are pretty marginal too. Nothing like big air-air front mount intercooler, but that's not possible with a positive displacement blower.
 
The positive displacement blowers are especially bad about heat soaking. They generally sit right on top of the engine valley, collecting the heat rising off the engine. The intercooler systems for PD blowers are pretty marginal too. Nothing like big air-air front mount intercooler, but that's not possible with a positive displacement blower.
It depends. Some PD intercoolers can work pretty well - like dual ones for each back such as the Edlebrock e-force. Mine, for example, was redevelpoed as dual pass due to the problems you described being an inhibitor on the amount of air a TVS blows.
One fact that on their side is that air-to-water is more efficient that air-to-air, and if you have a heat exchanger the size of a intercooler up front with a nice intercooler below the blower it can work pretty well. Although you are correct that its position is certainly not helping things.