hi 
i am new to this!
moved into  place with a fig tree.  
tree is mature with a bountiful crop this past season.  but its always droopy.   i water it a lot  stays droopy.  i give a break from water for a bit still droopy.  i  go the store get fruit tree fertilizer  still droopy.       its more droopy on the top then the bottom.  i live in stockton ca   its very warm here 100's in the summer 80's through fall
 

 

Root structure not sufficient to support foliage possibly, prune it lightly and check it.

You said "bountiful crop".
Sometimes bountiful crop also make the branches droopy.
Look at it again after the bountiful crop is no more.

Edit; Drought can also be a factor.
        No pruning also causes elongation of branches that droop easily.

Some of my trees do that but they are way smaller and in pots, more so in hot weather.

If branches are droopy, that is OK, and maybe a pruning issue. Older, unpruned trees tend to have longer branches that hang down. If the leaves are droopy (limp) that is a water issue.

We need pics of the leaves on top

Cory,
I don't see anything being wrong with your tree.
The heat will speed up dehydration of the leaves but after 9PM they restore the firmness. Think of Hydraulics system, if you reduce the pressure by lessening the fluid on the pipes? It's same with plants, figs have large leaves so it's more noticeable. Bountiful crop indicates that the tree is getting plenty and constant water source.
Be happy :) 

Agree with Fig Whisperer the tree looks fine. 

Agree with Enigma remove lawn under tree, it's a competitor. Put mulch.

You may want to condider 6 to 12 lnches of mulch from the trunk out to the drip line to conserve moisture.

Lack of water in the soil due to drought.
You need to water it as much as you can and immediately after watering to apply mulch like Jerry said,so water will not have a chance to evaporate.
Do not prune tree if you water and mulch because in high heat the dense canopy,maintain shade of base and so,water stay in the soil.