There are two things I can see that might be your problem; first is the temperature. When the temperature gets to 90 degrees F, plant processes shut down. Your tomatoes are causing enough shade to be able to continue minimal photosynthesis and uptake of water and transpiration. They look very healthy and that brings up the second possible problem...
You mentioned 'nutrients' which I call chemicals or fertilizer as plants make their own nutrients via photosynthesis but without balanced chemicals photosynthesis can not happen. Your plants look TOO good, grins. I am guessing you've used a high Nitrogen fertilizer meaning the Nitrogen is higher in proportion to the Phosphorus and Potassium. Great for lawns and leafy vegetables but not when you want reproductive growth.
Higher Nitrogen promotes vegetative growth and inhibits reproductive growth. You've said you've had lots of flowers then no fruit. Are your plants still producing lots of flowers? When did you see lots of flowers? What have you used for fertilizer and how long ago. How long has the temperature been in the triple digits?
If you used a high nitrogen fertilizer, 7-5-2 for instance or 16-10-10 where the number for Nitrogen is higher than the second two numbers, this would be the problem. The high heat in combination would only exacerbate the problem.
If you used 10-10-10 with all numbers even or better, 9-10-10 then it is probably the heat. Luckily for you, Austin, Texas has a lovely long season and we can turn this around. I've got family in this area and they've had problems growing tomatoes in the heat. I had them erect a 'shade' for their garden plot using shade cloth. 30%. It comes in differing percentages for blocking the sun. I also had them turn a fan on their plants as long as it wasn't raining. This helps move the O2 that is a by product of photosynthesis away from the leaves so CO2 is made more available to the leaves to do photosynthesis. That is one of the problems when the temperature rises. The photosynthesis increases with temperature but there is so much O2 made and hanging around the leaves that CO2 uptake is inhibited. Neat, huh?
You have to tell me what you've used for fertilizer as well as what if any compost you might have added. And how long ago. You will have to wait until your plants need more fertilizer and then we'll turn this around by using a lower Nitrogen fertilizer. No more compost! Great stuff but it does add Nitrogen. It is critical stuff to improve soil tilth, holds moisture but should never be used for fertilizer. It needs to be added to the equation for fertilizer but compost is not a balanced fertilizer. Pretty much just Nitrogen. Let me know if you have added compost and whether is was decomposed or fresh!
You have healthy healthy tomato plants that need to be kept in stasis until we can give them the signal to make seed/fruit. You have time. In fact, as the daylight hours are reduced going into fall that signal will help to tell the plants to make tomatoes as well. No more fertilizer until you send what you've used up till now, okay?
You'll have to watch for powdery mildew but the fan should help with that. If you get powdery mildew (white coating on leaves), let us know, easy to take care of. In fact you should start spraying this oh so innocuous mixture in another month. It is 9:1 ratio of water:milk. I put a couple of drops of dishwashing liquid per gallon of milk water for a spreader sticker. This works so very well I was amazed. But just for powdery mildew no other fungus. Thank you, Bamboo!! One of my cohorts on this site!
I should send pictures of this purple tomato I am trying this year. Not cherokee purple...the tomatoes are 1/2 dark black purple the other half bright green. Too weird. I think the purple develops in the light...get back to us with answers, hope this helps!