It depends on the plant, there isn't one set temperature. Many "heat intolerant" plants are also sensitive to photo period. As the nights get shorter/days get longer the plant responds accordingly. Days getting longer also means a warm up in temperature so those two things can go hand-in-hand. Cool season plants, such as sweet peas, naturally go dormant or finish their life cycle when it gets "hot". In extreme heat most plants temporarily shut down until things cool down. In the desert many plants are more metabolically active at night than during the day.
In my area sweet peas are annuals, we plant them in the Fall and they are gone by Spring.
Don't know if this is at all helpful. Instead of researching specific plants have you read a general botanical discussion of plant's response to heat?

As nmgirl says, photo period is a big factor too: many cool season greens, for example, will bolt not only due to increasing heat, but increasing light as well.

Nighttime temperatures surely also factor in, and since you're in zone 5 Arizona, I'm guessing you're at elevation and probably experience cool nights throughout the summer, like I do. This will offset any daytime heat.

I don't imagine you would notice any DAMAGE from heat in plants you try, just poor growth in the most sensitive ones, if that.

More than anything the heat designation will affect the TIMING (spring/summer/fall) of planting the seed.