In the time period I study, British ships had a galley stove somewhere in the forward part of the ship, usually under the forecastle deck with a chimney that would vent above and forward (square-rigged ships generally had the wind on the stern or quarter of the ship). The stove would be lit for cooking and extinguished otherwise; it sat on fire bricks to insulate itself from the wooden decks.

Sailors could smoke fairly freely, but were watchful of cinders and ashes. Water was very accessible to drown any sparks, and areas between decks were generally fairly damp in any case. Illumination would be provided by glass scuttles or glass crystals, by lanterns (the flame shielded by glass), or by opening gunports in decent weather. Otherwise, the tween decks were fairly dark.

Fire aboard ship was a constant danger that would be fought by buckets or fire hoses (connected to ship's pumps). Every gun crew had a fireman designated to quench sparks or burning debris from the guns or coming aboard.

Why would people want to keep tea warm? In any case, tea was a rich person's drink in the period that you're concerned with.