.NET production code profiling tool
Time has passed and there is another tool to list: CodeTrack. Usable without installation.
I don't know of any profilers you can use without installing them, so you may eventually have to come to some agreement with the client's IT department.
However, you may be able to get some insight by looking at .NET performance counters. Perhaps the service is doing excessive garbage collection for some reason.
If that doesn't yield any clues, you could use Process Explorer from SysInternals. It can be run without prior installation. The properties window has a Threads that will show you all the threads in the process as well as their running time, which could be helpful.