Sudden extemely high CPU usage

Last night I’ve got a notification from my shared hosting provider about extreme high CPU utilization – in peek times it reached up to 2,500% of my allowed power! The only information associated with that was that the file that consumes this enormous power is my WP index.php. I’ve asked the provider for more info but got none apart from I already known…

I have the lastest available WP and all plugins used installed and at least for 4-5 days before it happened no WP item was modified / upgraded, so definitely no new / modified script etc. could start running suddenly. I’ve reviewed the access logs, security logs and error logs and found nothing unusual. The traffic hasn’t changed dramatically.

I even took down the site for a couple of hours – surprisingly enough for most time CPU load was almost zero, but there were two peek hours with 600% load! Now the site is back online and I’m still reaching 300-500% of the allowed consumption.

I’ve just installed W3 Total Cache hoping it would reduce CPU usage but need to wait until some results are available.

Is there any way to investigate the root cause of the issue? The site address is http://www.fraudiq.eu.