hello,

i'm fortunate that i was also facing same issue.and here i'm able to give you some pointer.

Couple of things that you have to check and reply.first which version of sharepoint server installed in your machine, if i understand from  above messages its installed, either moss 2007 or wss 3.0

1.) are you using VM and wss 3.0?

2.) are you connecting to vm from same network or using some third party tool to connect?

now explanation.

there are so many cases which causes this problem.

3.) is there any timer services or jobs running to sharepoint sever or to the local databse which stores sharepoint.?
check if so than seprate them.

4.) what is the file size of your sharepoint date base.
check it must be incresing unpredictbly, if so check the backup and recovery modal u have applied for sharepoint server.

5.)If you your sharepoint log files are shaving in the c drive replace it in some other drive.

6.)check if there is any list exist in sharepoint which  gets updated at the time when cpu usages increased.

7.)check also is there any .net services which fetch data from sharepoint machine.

8.)check also if there is any workflow or event handler executing at the same time.

9.)No of end user interaction to the machine at the same time.

10.)check the features activated on your app and used at the same time.

11.)check if the cpu usages is very minimum at the evening or at non working hours.

12.) and also  if your machine is in shared network.


hope the pointer will help you!!
Regards
D

Here are my best thoughts:

a) Do you store any session values InProc - then check all the elements you store InProc. Although moving them to a more scalable SQL Server solution will help, don't do it unless you actually figure out the process hogging element.
At a later stage, after figuring out the faulty element, to release some process related issues - push the session to SQL server. 

b) Is the Worker process too less to handle the load? If you think so, increase the number of worker process in the application pool.

c) This is the best one - for it has helped me solve similar issues twice - the IIS Debug diagnostic tool. You can download it from here. The knowledge base article titled "How to use the Debug Diagnostics Tool to troubleshoot high CPU usage by a process in IIS" explains all the necessary steps that you need to take to figure out the issue.

d) And obviously you need to check if you some timer jobs that do the profile synchronization at that particular time. If you have it so, then please check the jobs

e) Have you though about Search crawls lowering the scalability of your application? Crawl loads are known to cause intensive CPU usages. The technet article titled "Manage crawl load" explains you what happens and how you should fix it. 

Good luck.