A TEC unit that uses the peltier effect needs a lot of power to create the temperature delta, with very poor efficiency. How will you power it?
The hot side of the TEC will get even hotter than your inverter is getting right now. You will have a lot more heat to deal with and remove from the area. How will you cool the hot side? How will you deal with condensation on the cold side?
Fans are more effective than you may think. You can purchase some PWM fans, used server fans are great if noise isn't an issue. Measure the temperature of the hottest components with and without the fans, and see the difference they make. Evaluate whether additional cooling is necessary using objective measurements, not based on how hot it feels.
Add quality thermal compound between components and heatsinks if not already present.