I have a 1.3.7 Zencart that gets 4000+ hits per day. The 2 servers I have put it on eventually start going down (downtime) with cpanel server status error: Disk /dev/sda6 (/tmp) 100 %

I was wondering if there is any tricks to optimize my site to store or record less statistics or run more efficiently to stop Disk /dev/sda6 (/tmp) getting maxed out.