My experience with tomatoes are that when the temperatures are extremely hot they will lose blooms and stop producing and it is a documented fact that they will do this. Blossom rot is when the tomatoe has formed and there is a black rotten spot on the end of the tomatoe where the bloom once was. This can be caused by not enough calcium in the soil and dry weather. Even watering will help with this. They like about an 1" of water a week. They can go with less but not much. Mulch helps with the evaporation of water and also helps keep the roots cooler in extreme heat.

The cloth should help screen the sun from scalding as long as the cloth is help up away from the plant like a tent and there is plenty of air circulation.

I made a shade cloth using garden stakes and double layered (folded in 1/2) burlap. It did serve to prevent leave scorching. However, once it's really hot (95 and up) day in and day out, there is nothing to do to make them set fruit. You might as well play out what you have on the vine and start thinking about fall Toms.

I've seen somewhere that a person used cheesecloth and it worked for them..they suspended it above and to the west side of the plants..it was supposed to keep the tom's fruit from getting sun scald..I'm thinking maybe they pruned a little too many branches exposing the fruit.
The blossom drop you're experiencing is from excessive heat..most toms won't set in high heat, though there are some varieties that do (or claim to)Arkansas Traveler,HeatWave II, Homestead, SolarFire..Sunmaster...just to list a few..
Google "Heat tolerant tomatoes" and maybe try some of them for a fall crop..I am..

Happy Gardening