There are always nay-sayers who essentially say "leave your Hyundai" alone as intended by Hyundai. I ignore them.
I applaud what you have done. I am on my third Genesis V8 ('09, '11 and '12 Rspec). In each case I was able to not only increase power using a cone filter at a level I could feel with my seat-of-pants dyno, but also increase gas mileage a bit.
I use only K&N filters. Many of the
aftermarket vendors include no-name imitation K&Ns in their kits. I have been using K&Ns since they first came to market. Originally, you were required to oil the K&Ns yourself. Now they come pre-oiled. I probably have more than a half million miles on K&Ns over many years. Never have I seen the urban legend claimed problem of oil transfer to MAF, even when we had to oil the filters ourselves.
Filter size is important. For obvious reasons use the largest filter you can find. I like the K&N #RF1040 which has a 4" mouth
.
Most vendors supply a model-specific under hood open airbox, which blocks under hood heat from the the air filter. This is difficult to create yourself, but you can create some heat shields around the exhaust manifold which will help reduce intake air temp.
On my applications I monitored ambient air temp. (dash OEM gauge) with intake air temp. (ScanGauge). Found the usual OEM differential to be in the teens (testing done on highway conditions with the car fully warmed). With a K&N cone and some creative heat shielding/intake air routing I was able to reduce this differential to less than 10 degrees consistently.
It is a good idea to take reasonable steps to reduce under hood heat. One little trick I have done for years not only on Hyundais but any other vehicle I own is to reroute the coolant lines to the throttle body so as not to heat the throttle body. Throttle bodies are "heated" by coolant so as to prevent icing, which can conceivably occur (temporarily) on a cold motor, high humidity, and closed throttle plate. This is a rare condition; and even then the coolant temperature is still fairly low. Don't block the coolant lines - just connect them together.
Another little trick is to change your thermostat to a lower opening temp. Presently, my RSpec runs consistently at 194 degrees; and I think it would run a bit better at a cooler temp say 180-185. Here is a forum comment on the subject by a Genesis coupe owner running a 3.8 like yours:
http://www.Genesis Coupe.com/diy-do-yourself/107499-diy-170f-thermostat-mod.html. It is more of a project on a V8.
Someone I am sure will chime in now saying that most power levels are achieved at a much higher coolant temp, say about 220-230F or so. That is true on a dyno or race car where underhood temps are very close to ambient. But in my opinion and in the opinion of many tuners (A. Graham Bell, for instance), more and better on-the-street power is achieved by reducing intake air temperature and under hood temp.