I guess a car fan is much overpowered for your application. It produces windspeeds making your pigeons "hover" at 80km/h.
All you need is a fan of a volume high enough to replace the air at a rate of 6 to 8 times per hour.
I suggest to use multiple fans of low airspeed and -pressure speed and high volume flow.
There are mains operated fans on the market with a diameter of 92mm. They deliver 88.3 cubicmeters/h at a noise level of 31dB. (price ~ US$15)
Reducing rpm and air flow for the car fan will definetely be higher in price.
Using two of them should suffice unless your pigeon house has the dimensions of a concert hall.
Boncuk