>>4018
>is there a fixed time when the trade cart leaves neverwinter?

Considering the quest isn't taken, the cart won't leave until someone takes the quest, but it may expire in a number of days or be re-evaluated.

>is there some public thermal bath in neverwinter and how much does it cost?

Of course there is! Well two ways, you can order a tub and hot water but that would get you a wooden tub to your room with buckets of hot water.
>>4001

The second way would be to visit a bathhouse, they're are many throughout the city and range from large private rooms with wine and fruit service, massage and oil, to public shared baths, basically a pool of replenished river water heated by an underground fire pit. The cost is 1sp for the lowest co-ed baths, 50gp for the highest end suites, but those will be a little walk across the river.

Close by, there is an inn with one available to guests but paid separately, 5sp plus 2sp each, room sized and semi private and they will take drink orders. Considering you have a room, the next option is a public indoor bath house on a parallel street north of Main for 2sp each, that one has "other services" as well but aren't sold together.

The Temple of Tyr has one, you may convince them to use it.

There's an open roofed bath, heated, refreshed with river water, southwest from the end of Main, it would be 3sp per person and is segregated between men and women.