This page explains how to complete the level 85 Endwalker quest "Warm Hearts, Rekindled Hopes".
This quest is available if you have completed the quest When All Hope Seems Lost.
Starting the Quest
Talk to Alisaie in Thavnair to begin the quest.
Survey the Designated Location
Go northwest to where the orange arrow is pointing in the minimap. Before you check on the Destination, there is an Aether Current to the west that you may wish to attune to. Then check on the sparkling Destination to proceed. There will be a cutscene.
Go to the quest icon on the map and check on Mehvan.
Search for Mehvan's Baby
Look downward to find Mehvan's baby. Go downward and check on the baby.
Have Alphinaud Tend to the Baby
Swim upward or hold the jump button to go above water. You can't summon a mount, so just swim northeast to the ramps out of the water, then go to the quest icon on the map and talk to Alphinaud. There will be a cutscene.
Speak with Alphinaud
Talk to Alphinaud to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Estinien to accept the next quest: Simple Pleasures.