To a degree, it should work, but only in the sense that a phantasm of a person shouldn't feel like a room temperature corpse to the touch, but in terms of fire scale heat, that could burn, I don't see it. . . .then again, you could make a phantasm of a warm tub full of water by that logic. . . .it's a very fuzzy area that's not actually addressed. . .
The spells are intended to make things so convincing they could fool you, so shouldn't necessarily be able to detect illusions/phantasms because they are always room temperature, so as GM you could say that "Feel" elements include appropriate temperature elements. . . .but the spells also specifically inflict martial arts damage regardless of what they look like when used to attack, so they cannot be burning hot or freezing cold, at best, if the GM decides it works that way, merely warm or cool to the touch as is appropriate to make the illusion/phantasm seem real.
It does seem that creative use of an illusion or phantasm could help with being out in the freezing cold, be it by making a tent (or perhaps a bath full of warm water), but the OP question of a bonfire doesn't seem to work. . .at best the bonfire would be body temperature warm, if the GM decided to be nice, it wouldn't throw off radiant heat as a fire would. . . .