"iexplore.exe" is listed as a running process, but not "IEXPLORE.EXE". The Kaspersky report always shows it in caps, as written by me above.
Does that make a difference?
Yes, I've been running Winpatrol for a short time, since reading a recommendation for it in another thread (possibly from you?). But I'm not yet fully familiar with its behaviour. It runs as a background process.
It hasn't given me any warnings about this iexplore.exe thing.
In F-Secure there is a check box for "don't display this message again" when the firewall flags an event, if I don't tick it then the message keeps reappearing, perhaps KIS has something similar to disable the message, that is presuming the message is harmless of course as adman 2 suggests, I would tend to agree with him as there was an IE 7 fix in the last round of updates although the iexplore.exe file is related to a few types of virus/trojans depending on size/location of said file, as skidzy says it's strange that KIS is reporting it in capital letters as a change in letter case is also indicative of virus activity.