Shabbos, Chapter 3, Mishnah 3. This mishnah deals with cooking that is not done on the fire itself, but by means of objects that have become hot, whether from the heat of a fire or from the heat of the sun.
Toldos ha'ur - an egg beside the kettle:
The mishnah rules: "Ein nosnin beitzah b'tzad ha'meicham bishvil she'tisgalgel" - one may not place an egg next to a kettle of hot water that was heated over the fire. Even after the kettle has been removed from the fire it remains very hot for a long time, and one who places an egg beside it causes it to be partially cooked ('gilgul' - roughly the consistency of a soft-boiled egg). Even though this is not the fire itself, but what is called 'toldos ha'ur' - something that became hot as a result of the heat of a fire - it is forbidden.
Toldos ha'chamah - cracking an egg into hot cloths:
The mishnah continues: "V'lo yafki'enah b'sudarin" - one may not break an egg into a cloth that was heated by the sun, so that its heat will cook the egg. Some explain that the intent is not breaking the egg at all, but wrapping it in the hot cloth so that it will be warmed by its heat. (Much like the familiar expression about an especially hot day, that "you could fry an egg on the sidewalk" - and even if it does not quite reach frying, it certainly reaches warming.)
Why is this forbidden? The Sages said that although it is permitted to heat things in the sun itself, since it is obvious and clear that this is not cooking with fire, they forbade heating something by means of an object that became hot from the sun: once the object is hot, it is no longer recognizable whether its heat came from the sun or from a fire, and since there is no way to tell the two apart, they issued a decree forbidding it.
"V'Rabbi Yosi matir" - Rabbi Yosi holds that one does in fact distinguish between something heated by the sun and something heated by fire, and therefore he does not accept the decree that is based on the assumption that the two cannot be told apart.
Burying an egg in sand or in road dust:
The mishnah continues: "V'lo yatminenah b'chol uv'avak derachim bishvil she'titzaleh" - one may not bury an egg in hot sand or in the dirt of the roads that has become very hot, in order that it should roast or be partially cooked.
The Gemara points out that Rabbi Yosi does not disagree in this case, but agrees that it is forbidden, and there is a difference of opinion as to the reason:
Sand and dirt resemble hot ashes, and one may not bury food in hot ashes on Shabbos because they are actual fire. Because of this resemblance Rabbi Yosi agreed that one may not do so.
Perhaps he will not have enough sand or enough dirt, and he will come to actually dig up dirt, a labor forbidden on Shabbos.
To summarize: The first Tanna forbids these things because of 'toldos ha'chamah' - the very fact that the object was heated by the sun creates the problem. Rabbi Yosi, by contrast, sees no problem in this, and he attributes the prohibition regarding sand and road dust to a different reason: either because of the concern that he will confuse sand with hot ashes, which are actual fire and a genuine problem of cooking on Shabbos, or because he may come to dig up more dirt if he does not have enough.