Throwing dry ice at the bottom of your case will have practically little benefit to cooling, you might lower case ambient temp by a degree or two but that would be about it.
The proper way to use dry ice to cool something (typically the CPU) is to have it cool water, which is then applied to the CPU in some fashion. That will give you lower temps, though is limited to your supply of dry ice and willingness to put more in (Cant imagine many people want to interrupt their gaming to shovel more ice into the computer every 10 minutes).
Cooling solutions like Dry Ice, LN2 and Liquid Helium are only temporary, they arent viable long term. Hence why they are only used to achieve extreme overclocks.