These files are executed in association with Windows Explorer, so the system does not allow you to remove them manually should you wish to maintain your privacy from any possible intrusion.
To overcome this 'little' problem you now have the Index.dat Analyzer tool.
Index.dat Analyzer is an open source program designed to inspect these files and delete their contents. Through a simple but attractive interface, the contents will be listed, showing some information for each item. To remove them, you can just select it and Index.dat Analyzer will do the rest.
The program removes the content, but not the file itself. Therefore it is recommendable to clean the system periodically