As an earthling this is probably the first thing you think about when you read about Mars - too hot for life in the day, too cold for life at night. But that makes way too many assumptions relative to _human_ life. It assumes nothing could be rigid enough to adapt to day and night extremes greater than Earth's.
It seems to me the greatest challenge to thinking about potential life outside this planet is being mentally bound to the constraints of life on this planet.
I always felt the same way about astronomers linking liquid water with life but then again where do you start if you don't use the only known instances of life in the universe as a template? Maybe it happens that there's a viable evolutionary path for sentient Nitrogen clouds but how would we know that?
Furthermore it doesn't sound too absurd that the very complex chemical constructs necessary for life would have a greater chance to stabilize in less extreme environments with a smaller temperature amplitude. Especially if you're looking for complex life and not merely microbes (which tend to be a lot more resilient).
Most likely because looking at extremophiles on Earth, you just need somewhat stable energy gradient and you'll find some life that draws energy from that gradient using weird chemistry.
Hardest to find for us because most of our chemistry research is geared towards carbon compounds around 20deg C, not sulfur compounds around 500deg C that dissolve most of our equipment in minutes.
Disregarding the possibility of life elsewhere that couldn't possible survive on Earth discounts most of the planets we know about.
So if survival of those life-forms depends on gravity, pressure or chemistry then we definitely should not rule out places where those are different than on earth, in fact that is to be expected. But temperature is a very important factor and the make-up of the star itself is also very important.
So it makes sense to check the likely places first before spending time and effort on much more unlikely places.
Some of these organisms also have novel ways of acquiring energy, so it seems like research like this is probably our best near bet for understanding how life can thrive in extreme conditions.
I'm having a hard time finding all the people stodgily insisting that only life exactly like Earth's is possible through the hordes of people screaming about how it might not be. Everybody already knows that life might not be exactly like Earth life. Any illusions to the contrary have been shattered by Earth life itself and the concrete existence of extremophiles, which are themselves already not what most people imagined "Earth life" to be.