This is less a brewing method than a decision that ruins or preserves a pot of filter coffee, and it is made at the point of purchase.
What a hotplate does
It holds the carafe at 80 °C or so by applying continuous heat from below.
Coffee is a solution of volatile compounds, and heat drives them off. Held on a hotplate, a pot loses aromatics within minutes and begins developing bitter, stewed, burnt notes within about twenty. After an hour it is noticeably unpleasant.
The glass carafe also picks up scorched residue at the contact point, which contributes its own flavour.
What a thermal carafe does
Insulates. No heat is added, so nothing continues cooking. Temperature falls slowly — a good vacuum carafe holds a pot drinkable for two to three hours.
The practical rule
If the pot is drunk within twenty minutes, glass and a hotplate is fine.
If it sits at all, thermal, or decant immediately into a separate insulated jug.
Buying
Machines usually come in both versions — Moccamaster’s KBG is glass, KBT thermal; Sage offers both.
Decanting from glass into a cheap vacuum jug achieves the same thing for very little.