I question how hot a 1zzfe can really get under the hood. I think the need for a scoop or cowl wouldn't help much IMO. Perhaps getting some tubing leading from the front (like the bumper, very subtle), to the engine compartment would help. This would cause an environmental ram air into the engine compartment. Since you are moving, the cool air comes in, while the hot air gets pushed out. Also, no cutting, no aesthetic changes, and no painting.
Or you can change the fan, think of how a computer case uses tubing to suck outside air in, throught the processor and back out again.
I also think that some m3 fender gills could help and not destroy the looks too too much. I agree with Bitter, the scoop doesn't look right on a corolla. But...I am also a firm believer that there is a difference between ricing a car and souping up a car. For you to put a scoop because you need it, IMO, it doesn't become a rice accessory. Its not an accessory for the bling bling on your car but rather for a purpose.
If you have an 8th gen corolla, the outsides of the hood dip in a little bit, perhaps some really subtle subtle scoops or gills on each side would help.
Take a look at what fish said about the exhaust headers, they are thin and more prone to cracking. So..I don't know if you have stock headers but...
This might all sound like bs, but hope this might add some creativity to your problem solving.