When Ad-Aware scans, it creates the AAW.TMP file if it wishes to place something in there. While it is scanning, it is effectively probing files on your system.
What AVG is telling you, is something is trying to open an infected file. So it's not so much Ad-Aware is harbouring Trojans, but that AVG is preventing Ad-Aware opening the files.
You need to establish which files are being probed when this happens and if you are at all suspicious about their source or integrity, get rid of them.