What things we should consider while choosing humidity temperature sensor for battery operated applications?
I'm looking for an ideal sensor for low power (battery powered) application where accuracy could be around 0.2C for temperature and 2% for humidity
Is there some sensor where we can set lower and upper limit and it can trigger uC when it reach to that limit?
I would offer a handful of 'must knows' based on working with a handful of different humidity sensors. What I am telling you is not the end-all on the subject and others may have much more experience and weigh in here as well.
First, I say that you should get a grip on what RH% is and then learn something about approaches to measuring RH - lots of reviews/turtorials/introductions on line. Maybe you are already comfortable with that subject..
Next, I would say that you need to actually validate that the sensor works as you think. That means testing it against standards. For RH, you can look into the salts method and you can do this yourself. You can also calibrate the sensor (or, more accurately, know how to modify the measures you are reading) if it is systematic. For temperature, I know less about standards (beyond freezing and boiling points of water) and it might be that you validate and calibrate against high precision devices, be they "traceable" thermometers or people who really know how to use a high accuracy meter and a high accuracy thermistor (leaves me out

Along with this last point, you need to think about harsh environments - most/all of the common digital RH sensors that I know about do not handle the extremes well. If left in very humid or very dry environments, they suffer and they may actually need rehydrating or dehydrating to reclaim their former accuracy. Additionally, you can't just assume that the will last for 20 years and I don't know how to evaluate their life expectancy under different conditions.
There are digital sensors that have their own alarms which you can program (e.g.,
https://sensing.honeywell.com/alarms-on-humidicon-tn-009060-3-en-final-07jun12.pdf and
https://www.microchip.com/wwwproducts/en/AT30TS750A). Depending on what you want to do when temp/RH goes above or below your limits, you may not need a controller at all.
If you do use a controller, you have a whole new set of low power aspects. So, do you want to wake up every 10 minutes, read the sensors and decide what to do or ? While I know less about the low-power issues, there are a lot of dependencies and you may need to specify a little more about what you want to do.
Hope it helps.