Having the PC case open may actually cause worse temperatures. This would, of course, depend on the design of the case and airflow.
The stock cooler on my 2500k keeps it nice and cool--never gets warmer than 66C with ~20C ambients.
80C is warm, but keep in mind, CPU stress tests tend to drive the CPU more than any typical "real world" use--so you probably won't ever hit temps that high with, say, gaming, for example.
Have you ensured that the mounting pegs are firmly secured down? Also, did you apply the TIM, or did you use the pre-applied TIM that came on the stock heatsink?