My cukes can get stressed during July and August, the hottest months of the year in Michigan. Will black weed barrier work as shade cloth or will too much heat build up behind it and further stress the cukes?
It depends on the weed barrier. If the weed barrier is too thick it would diffuse too much of the sunlight. Your cukes need the sunlight.
Let me preface this by saying I haven't done this. If you could somehow arrange the cloth with trellises or poles in a manner so that the plants would receive some shade for the hottest part of the day (12 - 2?) it would lower the temps a bit during that period.
If you already have a trellis setup you could probably attach additional poles at an angle with the weed barrier cloth zip tied to those poles. Maybe like a window awning, but with the bottom portion loosely attached so that it would move with the wind.
Your intuition is correct, it will retain too much heat. It's both black in color and too tightly woven to allow much air movement. Charles answer is also correct, the amount of light the material lets pass through is a significant consideration. The plusses are it's cheap and readily available :) I spent 2 weeks asking myself the same question earlier this spring and it finally dawned on me :) Burlap is a natural choice. It's light in color, has a course web that allows better air flow, and it's price and availability is very similar to landscape fabric in most garden departments at big box stores.