What does “there” mean in the last sentence?
Solution 1:
Yes, it appears you are reading it correctly.
"There" appears to refer back to "hers" which refers back to his...sunburned hands." So the warmth is there, in her hands, and it filters (moves as if through a membrane) to his hands.
There is a subtle inconsistency too: "hers" refers to "hands" (plural), but the warmth filters from her "hand" (singular) to his.