I have improved Meyer's lemon and Kaffir lime growing successfully in large pots on my sunny, CA concrete patio. I have had success and near failure. They have both always produced for me, although the limes are small and insignificant-- I use this tree for it's aromatic leaves in Thai cooking. The near failure I had was when I wasn't watering enough. I now have them on irrigation so they are getting consistent water, and they are both very happy for it!

I have also had success including fruit yields from potted blueberry shrubs, strawberries, and cumquat tree. All on the same hot & sunny patio.

If it is too hot, consider elevating the planter off of the ground with a pallette or two 2x4's to get some air flow under the pot to cool the plant roots.