Out of Disk Space Issue

On 15th April, when i login to my hosting account and found that my all 30GB Disk Space is finished suddenly. I got shock and check the disk usage utility and found that one of my site is using 29GB alone. When i further explore the file manager i found that there are more than 100 Core files with four digit (e.g Core XXXX) and each core file size is 120mb to 145MB. So i asked my hosting provider (Siteground) to look there and they concluded that this may be the cause of plugin (i use Wordpress). I don't know which plugin generating these files or its some kind of virus, as I didn"t install any plugin in last 2 to 3 months as I remember. So i disabled all plugins, but core files were still coming. God knows from where. I updated my ticket with siteground and explained its not plugin fault and representative from siteground blame the theme developer. I asked the theme developer to look there and he said, "My theme is running very well on all other sites as i didn't get any complain from anyone so contact your hosting" After 15 days of trying each support, i didn't get anywhere. Siteground blaming to theme developer and theme developer is blaming to siteground. One is accusing server fault, while other saying that its theme fault. Good news is Cron job is active in my hosting and it's deleting Core files every 30 mints. Still in 30 mints more than 25+ core files are coming. Its not permanent solution but its giving me time to solve this issue. So, if anyone who have any idea how to get rid of them, please help.