Find out why WordPress woocommerce website is overclocking CPU

Hi There

Firstly I want to note I am looking for a UK based developer on this

The problem:
I have a complex wordpress/woocommerce website and it is overclocking and hitting the CPU resources making it get limited with very little traffic
The mission is to try and figure out what is doing this and see if we can fix it
Many plugins are integral to the build so just switching a plugin in most instances wont work
This can't be tested on the live website, that is the sole income provider for my family, that can't be messed with, however I have a mirror of the website on a subdomain
Updating everything is a house of cards so I would rather avoid that if possible and focus in on the issue at hand before making any decisions.

Then we go onto stage 2 and see if we can fix it. Where I will also require a development log of any changed files.

Obviously until you figure out the problem we can't assess a price for the fix so please quote me your hourly rate and how long you think it will take you to assess it. If you are the problem finder person and not the fixer that is okay too.

Please give me a brief idea of the tools you would use or something else to show me you are human and have read the description in your bid.

PS: it is not a virus or hack, it is a newly launched website.