I have a windows service written in C#.Net. When the service is started, I spawn a new thread as shown below
new Thread(new ThreadStart(Function1)).Start();
If you're using Windows task manager to try to work out the memory used, it's likely to be deceiving you. Memory used by the CLR isn't generally returned to the operating system as far as I'm aware... so you'll potentially still see a high working set, even though most of that memory is then still available to be reused within the process.
If you let the service run for a week, do you see the memory usage climb steadily through the week, or does it just increase in the first day, and then plateau? If so, do you definitely view this as a problem? If so, you may need to put your second task in a separate process.
Trust the garbage collector and stop worrying. 150 megs is nothing. You aren't even measuring the size of the file in that; most of that will be code.
If you are concerned about where memory is going, start by understanding how memory works in a modern operating system. You need to understand the difference between virtual and physical memory, the difference between committed and allocated memory, and all of that, before you start throwing around numbers like "150 megs of allocated memory". Remember, you have 2000 megs of virtual address space in a 32 bit process; I would not think that a 150 meg process is large by any means.
Like Jon says, what you want to be concerned about is a slow steady rise in private bytes. If that's not happening, then you don't have a memory leak. Let the garbage collector do its job and don't worry about it.
If you are still worried about it good heavens do not use task manager. Get a memory profiler and learn how to use it. Task manager is for inspecting processes by looking down on them from 30000 feet. You need to be using a microscope, not a telescope, to analyze how the process is freeing the bytes of a single file.