The new PSU has two fans, my CPU has a fan, and there's a big fan on the back of the case. Also my tower is in a relatively cool environment.
Keep in mind that those are all exhaust fans -- the fan at the front would draw extra air into the front of the case, helping airflow.
without the front intake fan, it is harder for air to get cool air sucked into your system, which means that there is less warm air leaving your machine raising the overall temperature a little... But in most cases, it will still be cool enough.
However, if you do see your system start getting unstable (spontaneous crashes, weird graphic corruptions on the screen, memory errors) that the most likely cause if overheating which can be addressed by adding a new front fan back in.