I suppose it could. It's possible fuel filter is restricting follow. It may or not effect idle or low speed, but then restrict fuel at higher demand (RPM). A lean fuel air mixture would cause engine to run hot. Not sure how ECU would react.
I've read here in mud a few times of fuel issues with the 06, in-which the fuel pump was to weak (low fuel pressure). This seem to cause issue most notable ascending mountain HWYs. A fuel pressure test may or may not be reveling of fuel restriction.
I'm looking at the maintenance history at this moment on a 06LC. It seem it had P0420 pending June of 2011 at 96K, T-belt & CAT(s) replaced. Then August of 2011 Fuel pump replaced??. I'll need to get some more color on this 06 and it's P0420, but seem they replaced CAT and issue returned. Then never returned after fuel pump replacement (not yet sure fuel pump was replaced). Driver first reported loss of power ascending mountain HWYs starting in 2008.
Using only OEM parts specific to the 100 series and year correct, whether in a Toyota box or not, is always best practice. I just purchased & installed a new OEM Fuel Filter in the 07LC, even though I had a NAPA FF sitting on the shelve.