The spell seems to be written with the idea that the huge creature would take "waves of heat" damage on the caster's turn if the creature were in range of the "waves", and "passing through" damage on the creature's turn if they moved through the wall of fire. By a simple reading, the creature would take the "waves of heat" on your turn, and "passing through damage" on the creature's turn. The same would repeat the following round if the creature was still occupying space in both the "waves" range on the caster's turn and "passing through" range on the creature's turn.

This post is similar, though dealing with a different issue.

After re-reading the spell description, it does appear the creature takes "passing through" damage on your turn (because it's "if you evoke"). With that in mind, I think the first round, the creature would take "passing through" damage on the caster's turn, and then on their turn, if they don't (or can't) get out, "passing through" again. On subsequent rounds, I would treat is as above.

Rules as Written are Unclear

The Force Cage spell states (PHB, pp243)

When you cast the spell, any creature that is completely inside the cage's area is trapped.

And then separately:

Creatures only partially within the area, or those too large to fit inside the area, are pushed away from the center of the area until they are completely outside the area.

Given that these are are two separate sentences, the "too large to fit" clause may or may not be directly tied to the "when you cast the spell" clause. If it applies to both at time of casting as well as during the life of the spell then the creature is shunted (if it is two sizes larger than the cage - see squeezing rule.) If it only applies to the cage creation, then it raises the issue of a creature being in too small a space (see below.)

If those two sentences are supposed to be directly related, it changes the interpretation and then allows for use of Force Cage to autokill something. There are no real rules for this, and this question on polymorph may be related with regard to too small a space. See the Concerns section below for more information.

Squeezing into a smaller space

On the chance that the polymorphed creature is just one size smaller then the creature itself, the Squeezing rules would come into play (PHB, pp192)

A creature can squeeze through a space that is large enough for a creature one size smaller than it...It has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it's in the smaller space.

Concerns

There are two concerns that you should consider when determining use of this at your table:

1. If you choose to read the Forcecage text as not applicable post-casting, then you have created a neat effect to instantly kill a creature. This could become very powerful if you have a group that is able to do this. However, this is also using a 7th level spell slot (along with a 3rd) - and may not be as unbalanced as it seems. This is similar, but not identical, to the idea of polymorphing into a tiny creature to be eaten or go into a larger creature and then end the polymorph so you "burst out" and kill the creature. There are no RAW rules around this and allowing tactics like this potentially creates a slippery slope (although not as great when you consider the 7th level spell cost for Force Cage.)

2. If you choose to go with the interpretation of being shunted out, you are risking devaluing the Forcecage. The odds of this happening are small as it is unlikely to be used against the party by an enemy.