How do you clear temporary files in an ASP.NET website project?

All you need to do is stop IIS from Services, go to c:\Windows\Microsoft.NET\Framework\v4.0.30319\ or respective Framework directory, open the Temporary ASP.NET Files and delete the folders

What happens when we delete these files? Is it safe?

Yes, it's safe to delete these, although it may force a dynamic recompilation of any .NET applications you run on the server.

For background, see the Understanding ASP.NET dynamic compilation article on MSDN.