If all the steam from a bowl of boiling water is collected, after all the water boils away, would the steam's temperature go up?

I'm not quite able to understand what the question is. Are
you collecting water separately as it evaporates from the bowl, or is the steam
collected in the bowl which is a sealed one?

In the former
case: When you collect the steam as it is produced with the water in the bowl boiling,
there will be no change in the temperature of the steam whether it is collected at the
beginning or is the last bit of steam collected when the water is getting
over.

In the latter case: When the steam accumulates in the
sealed bowl, as you continue to heat the bowl, more of the water will turn to steam but
the steam produced increases the pressure in the container. This results in an increase
in the temperature at which water turns to steam. As heat is introduced into the
container the temperature of everything in the container, the water and the steam,
increases. The amount of steam and the amount of water present in the sealed container
is in a proportion which maintains equilibrium between temperature and volume. The
temperature of the steam here will go up as more heat is
introduced.