In order for a fan to draw air ACROSS the area to be cooled the inlet zone must be on the other side of the heat sorce so that the cool air flows across the heat sorce and out thru the fan. In the case of the engine room the air inlet is the entire bottom of the car along with the "airbox" side vents behind the doors and any other leaks at the front of the engine.
The problem is the fans will draw air from the closest sorce and the air flow will be the shortest distance possible. This will be the area directly in front of the fan. The resulting air flow path would be up from under the car directly in front of the fan, thru the fan, and out of the car.
This would not be of much help cooling the top of the engine room in the area of the top heat vent where all the heat is comming off the headers.
Drawing a large volume of hot air out of the top of the engine room, with the resulting air flow comming from the bottom of the car, across the headers and out the top might be a better solution. To do so would require mounting a fan over the rear clip top vent.
The fan and the fan motor would need to be able to stand very high temps in this location.
The Hall CANAM cars had the bottom of the car sealed with skirts. This caused an low pressure area to be developed below the car with the resulting down force.
A better example would be the Lauda Grand prix car that was run in Belgium in 1979. This car ran a huge fan off the back of the gearbox. The airflow was down thru water radiators above the motor from vents in the bodywork above the Flat 12 that alfa was using it that car. Then out the back thur a big hole behind the gearbox. The bottom of the car was sealed with skirts. The big lie was this wasn't a moveabe aerodynamic device, but was a engine cooling fan!
If I remember right it ran at engine speed and was about 24inchs in diameter!
I bet that fan had to consume 50hp!. As the revs went up the car was sucked down to the ground so much so that when he hit it in the pit lane other teams began to complain about violating the min ground clearance rule. Nicky didn't like the fact that he had to put the car in neutral, break the car, and hold the revs up at the same time into and thru a corner or all downforce was lost at just the time he needed it. The other drivers didn't like the setup because it tended to pick up EVERYTHING off the track and shoot it out the back at about a millon miles an hour right into their faces if they tried to pass him.
Mario hated it because it was FAST and he lost the poll and the race to lauda.
Oh and after Lauda won that race, the car was banned for the next race, and Mario went on the win the title.