An SSD should be considerably quieter than any mechanical HDD - they have no mechanical parts, which are what generate the sound.
An SSD should produce less heat as well; there are no mechanical parts, so no heat from friction, and typically SSDs consume less power than their mechanical counterparts, so should produce less heat that way as well.
Whether this will make a difference overall in your laptop or not is another matter entirely, based on far to many factors to give you a simple answer. I'll try, and here it is: Probably.
In a desktop (I have little experience of laptops in this regard) a (healthy, well cooled) HDD typically runs at about 40-50°C, CPU about 50-60°C and a strong GPU typically even higher. So the HDD is hardly the hottest part of the machine.
So changing it with an SSD probably will not help with heat a lot, but obviously with less heat from the drive the other components may be easier to cool because there's less thermal energy in the machine overall.
Conversely, I'd say a not-brand-new HDD can often be the most heard component of a desktop. However, they do tend to be placed near the front of a case, so it's hard to say they are really the loudest. Simple question - can you hear your hard drive when it's working? If yes, then an SSD will help by removing that noise entirely.
And, potentially, there's also a side-effect from having (potentially) less heat in your laptop from a cooler drive; the cooling system (with its probably loud fans) has less work to do and so may be quieter.