No, cases are made so that air traves into and out, creating more pressure and more flow (if done right). With the case open, the sensors may record less heat, but components may not be getting cooled as well. It shouldn't really be a problem unless you are doing heavy stuff like playing games, etc. Do you notice anything getting hot?
Run MemTest Memtest86+ - Advanced Memory Diagnostic Tool
- on each stick of Ram, one at a time until you get errors. It takes a while. There are a certain number of passes you need to let it go for, think the number was 8 or something.
Are you having a memory error or a general hardware error?
Are you overclocking anything? If so, reset your BIOS back to normal.