Answer: The Baal Hamaor (Shabbos 16b) writes that chazal decreed that we must eat hot food on Shabbos as part of oneg Shabbos. One who refuses to do so is suspect of being a heretic. The Rema (OC 257:8) quotes the Baal Hamaor though clarifies that it refers to one who believes that it is prohibited to eat hot food on Shabbos. R’ Moshe Stern (Baer Moshe 1:1:2) explains that as the Karaites denied the Torah Shebaal Peh, they sat in the dark all Shabbos refusing to leave any flames lit (See Ibn Ezra, Shemos 35:3). By eating hot food such as cholent on Shabbos one is protesting against this belief and demonstrating one’s belief in chazal.
R’ Nissim Karelitz (Chut Shani 28:8) notes that the Rema (OC 257:8) refers to it as a mitzva rather than a takana (decree) while the Mishna Berura categorizes it as a minhag that one should be particular to keep.
R’ Karelitz writes that even one who drinks a hot drink on Friday night that was insulated in a thermos flask has fulfilled this minhag, though it is ideal to have hot food during lunch.
The Magen Avraham (257:20) and Kaf Hachaim (OC 257:49) note that if one can’t eat such food then they must avoid it as it doesn’t serve as their oneg Shabbos.
In conclusion, there is a strong minhag to eat hot food such as cholent on Shabbos, though if necessary, one can fulfil this minhag by having a hot drink.