My daughter bought a used 04 Quest SL (CarFax says she is the sixth owner! )
It is missing the plastic engine top cover. With the summer temps testing 100 deg here the engine seems to be running hot. Does anyone know if that cover is only a decorative dust cover or does it affect airflow from the fans across the engine? She's a single mom and doesn't want to spend money on under-hood decorations if it's not needed.
Not sure HOW hot it's running because she's also afflicted with the partial gauge failure that seems pretty common with these.

Those covers are there to deaden sound and make the engine bay look more appealing. There's no problem leaving it off.

If your engine is running hot (how hot? did you pull coolant temp from OBDII?) check coolant level, radiator for clogging, fans, thermostat and pump. It is not unheard of pump vanes rusting off and thermostat failing. If the previous owner had a rad leak and tried to fix it with sealants, the entire cooling system may be full of crap and clogged.

04s are also notorious for ECU housing corrosion, so check the ECU condition. If there is corrosion, you should clean up the housing, see if there are any through holes, and apply lots of rustproofing between the housing and mounting bracket to keep the contact area free of moisture.

IACV coolant bypass is another good idea which should be on the priority list.