Question

for evaporation to take place do heat is needed to be applied or the molecules of water gain the required heat by itself? By heat I mean small amounts of heat not large, that is, without any application of heat by external means can water evaporate?

Answer 1

they gain required heat.
no heat supply is needed.
yup.water can evaporate with small amounts of heat even with a gradual absorption of required energy...

HOPE IT HELPS.

Answer 2

yes it can happen with the help of potential energy which gets converted into heat energy and the liquid gets vaporized .
in the case of water , when external heat is applied , it is known as evaporation.