analyzing time series temp data

I know some statistics but this is beyond me. I have a set of temperature measurements that were recorded at set intervals. When a certain condition occurs these measurements become constrained to a small range of temperatures. I have to be able to consistently identify the start and end points of each time this condition occurs. The kicker is that there can be the occasional fluctuation in temperature during the condition and I have to have a way to overlook it. I've started looking into time series analysis but it is something I've never been exposed to and there seems to be a lot of content involved. One thing I've noticed though is that a lot of what I've read about time series analysis assumes a random process, but I'm pretty sure that what I'm looking at doesn't qualify as such. I was hoping that maybe someone could maybe point me in the right direction. Something as simple as a term or method that I could look up and use as a starting point. Thanks.
If you're modelling the temps then it is likely you're using some sort of smoothed moving average? In this case then you should be able to calculate upper and lower confidence intervals. Then, if the deviant value falls within the range you're good. If you're not doing this, then perhaps a good start to research is ARIMA forecasting?
Thanks for the answer. I haven't really been able to try give ARIMA a thorough lookover yet, but I think I'm beginning to get an understanding of it and what it does. I haven't been able to try anything with it yet, but I've begun learning R so that I can play around with it.

I think your answer overall has potential for my problem. But, after rereading my original post I'm thinking that I may not have been clear enough in my description. Fortunately, I've learned enough R to plot my raw data which makes things clearer:

Basically, you can see several places where the data becomes relatively constant (with some noise) at about -1.4, and I need to identify them (when they start and end). Each data point is 6 minutes apart. Another thing that I'm wondering is should I be considering the precision of the instrument (0.5 degrees Celsius in this case)?

Is the ARIMA method something that I should still be looking at for this? Or should I be focusing my attention on a different method(s)?