Samuel Taylor Coleridge was raised in a time when the only heat provided came from a fire—in this case, in a fireplace that is covered by a grate (or cover), to keep stray sparks from flying out to start a fire, which was a grave concern with fireplaces during that time. (Fires started easily and were hard—or impossible—to battle.)
In his poem, "Frost at Midnight," Coleridge is alone in a room (at his cottage), except for the company of his infant son, sleeping in a cradle next to him: everyone else has gone to bed. It is so quiet, that the silence disturbs him. He is in a pensive or thoughtful mood, and his eyes are drawn to the fireplace, where he sees a "film of soot fluttering on the bar of a grate." After writing the poem, Coleridge attached a note to explain his use of the word "stranger," which was common in that day to refer to this film made up of soot: it was traditional in England to believe that seeing such a thing (superstitiously) announced the arrival of "an absent friend" and the sooty films were called "strangers."
The second reference also speaks of "strangers," but these sooty films were those he often saw in the fireplace grates at his school. In those days, Coleridge still believed in the power of the "strangers" in the fireplace. He would watch them at night and they would "lull" him to sleep—where he would see the familiar sights of home in his dreams; the "strangers" would be there—accepted by his "believing mind" that seeing the "fluttering" soot would bring those he loved to him there at school; "presageful" meant that such a sight (seeing the "strangers") had the power to foretell a coming event ("the arrival of an absent friend"). So this was when he was still a "believer."
How oft, at school, with most believing mind,
Presageful, have I gazed upon the bars,
To watch that fluttering stranger!
The next day when he should have been paying attention to a "stern preceptor's face," (teacher), he was only pretending to listen to the lesson for every sound in the room would grab his attention: he was homesick and desperately wanted "an absent friend" to show up at the door, most especially his deeply-loved sister:
For still I hoped to see the stranger's face,
Townsman, or aunt, or sister more beloved,
My play-mate when we both were clothed alike!