I can find a few references here and there to it being a chariot or something, but I don't just want to take any old lackey on the Internet's word for it. What exactly did they think it was?
Pseudo-Hyginus, Astronomica 2. 13 (trans. Grant) (Roman mythographer C2nd A.D.) : Sol [was the] first among the gods made use of the quadriga [4 horsed chariot]."
A quadriga (Latin quadri-, four, and iugum, yoke) is a car or chariot drawn by four horses abreast (the Roman Empire's equivalent of Ancient Greek tethrippon):
and you see in this image, it is most definitely a chariot.
Ok, it was a chariot. Where's all that light and heat coming from?
He seems to have some sort of diadem, helmet, or whatever.
Valerius Flaccus, Argonautica 4. 90 ff (trans. Mozley) (Roman epic C1st A.D.) :
"Sol [Helios the Sun] puts on his diadem of myriad rays and the corselet woven of twelve stars [the zodiac constellations] and bound by the belt which athwart the rain-clouds shows for men its many hued bow."
Nonnus, Dionysiaca 38. 90 ff (trans. Rouse) (Greek epic C5th A.D.) :
"He [Helios] placed the golden helmet [of the Sun] on Phaethon's head and crowned him with his own fire, winding the seven rays like strings upon his hair, and put the white kilt girdlewise round him over his loins; he clothed him in his own fiery robe and laced his foot into the purple boot, and gave his chariot to his son."
You can also see the diadem in the mosaic.