My company has around 20 servers which we want to operate in an underground room, where the temperature over whole year ranges from 5°C to 28°C.
The only thing I am worried about is that in the summertime, the place will be relatively humid, around 80% RH. Will this cause a big impact on the stability of 7x24 running hardware OR shorten the life span of the servers?
Check the server specs. They should (or at least big OEMs like Dell, HP and IBM do) come with operating ranges for temperature and humidity.
Three things though:
Putting servers in a room that's not climate controlled seems like a bad idea in general, and I wouldn't do it. This specific room sounds incredibly bad, like it may as well be a kill room for electronics.
At 5 degrees Celsius and 80% humidity, you will run into issues with condensation occurring, and water condensing on your electronics will cause hardware damage.
At 28 degrees Celsius and 80% humidity, this specific room sounds like it is probably going to overheat your gear, which will either damage it, or cause it to shutdown to prevent damage. The room will get hotter as a result of having electronics running in it, and without a way to dissipate the extra heat the gear produces, you're essentially creating the same effect as an oven.
High humidity will probably compound heat issues, because of the greater energy it takes to heat or cool humid air - it will take longer to heat up initially, but once it heats up, it's going to be much more energy or time-intensive to cool down.
Regarding the temperature range discussion brought up in the comments, there's an older thread on it, here. And it's all well and good to say "Google does [blah]," but Google also runs an expected failure model on cheap, commodity gear with many millions of dollars invested in their custom software to make it work. What Google does is not applicable to the vast majority of situations. (Such as asking about running 20 servers in a non-climate controlled room that wasn't designed with servers in mind. For example.)
Ok, here we go. I would absolutely not be concerned with temperature IF that is allowed for the machines, same with humidity. Modern servers support up to 47 degree ambient temperature and even old ones are made from components that are mostly also used in tower servers and allow ambients above 30. Intel and Google studies show no bad things happening.
Most important is to check what he manufacturers allow.
The problem is secondary stuff, MOSTLY USV - Batteries may not like this temperature.
The other problem you may have is delusion about what temperature IS. The underground room may have a low temperature because it is shielded from sun etc., but that may not give you a VERY big amount of dissipation - so you may simply heat that up VERY fast the moment you actually emit heat in it. My own server room is in the basement of our offices - well, 1 meter over ground, 1.5 meters below. NICE cool room. 4 servers and it heats up. Why? Because it is mostly cool because it is isolated and the ground is cool, but at the same time the heat does not dissipate in hugh amounts. For 20 servers that LIKELY does not work - you will overheat the room without active cooling component, which costs have to be factored in.
In our case we are installing air conditioning now and will ramp the excess heat into the house heating system ;) We also removed all batteries from the room (external large USV installed) and will increase ambient temperatures in the server room to the 40 degree level as we replace servers. That is still way below what the manufacturer or our hardware allows (47 ambient) but it will make active cooling QUITE efficient - we never had that temperature outside, and cooling with a cooler outer side is more efficient.
If you NEED active cooling, then humidity is a non-issue anyway as air conditioning can remove humidity.
So, the main question is - how much heating do you create, and that is directly the power consumption of your servers. Assuming 200 watt per server you run about 4kw. That likely is above your dissipation capacity.
So, the whole thing is not as easy to answer. Anyone focusing on temperature here so far totally forgets that temperature is not absolute, it is a balance between emitted heat and dissipation to environment. And the current temperature may have no meaning the moment you add the servers. It is unlikely you can add 4kw energy to that room without getting into active cooling of some sort (and air replacement is active cooling unless you manage to create the airflow just by heat differential - possible, but that requires building the building in a very special way).