Symptoms
After the go-live of the SharePoint 2013 intranet site with a K2 SmartForms web part that included a Form with a K2 Worklist control, there were about 100 users logging into the new site. However after about 20 minutes when (we're guessing) more than 400 users opened that site, eventually that web part stopped loading and it seemed like the K2 server was under extreme load, the K2HostServer.exe was running at between 0% and 70%, sometimes even spiking at 100%. They had to force kill the process to make things start to work again.
Diagnoses
After the investigation of the K2 Host Server error logs, we found 4 (unrelated) errors. We solved one error during the meeting on Thursday night when the ticket was logged (SP Group Provider out of date), then logged 3 additional tickets to solve the other three errors.
Resolution
After solving the other three tickets and changing the refresh timeout of the K2 Worklist from 1 minute to 5 minutes (default), it seems like there is less load on the K2 Host Server in production.
After we did our performance test for an hour (using Windows Performance Monitor) we noticed that the K2 server stayed relatively idle (at around avg 30% CPU load and 20% RAM load) and only spiking every now and again when there's something to do, like when a lot of users started opening the SharePoint intranet site and the worklist control gets loaded inside the SmartForms web part.
Most of the load was handled by the SQL server however (which also servers the SharePoint intranet site) and it will be upgraded over the weekend, I suppose this has been done and both K2 and SQL servers are able to handle the load now.