It should be fine without extra fans. As you said, it will be in a cool room as well. That will help. I would always monitor the temperature every now and then.
The site runs on WordPress and uses Woo Commerce. I ran a whois is on the domain. All the information is protected. Not a bad thing but unusually for a company to hide information like that. I'm not sure really. There's no terms and conditions page. It's pretty sketchy on first impressions.