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Tomatoes can't pollinate if the daytime highs are in the low 90s or above; the pollen is not viable. Same problem if the nighttime lows are above 75.

If temperatures are below 55, pollination can't take place either. Using Blossom Set spray enables fruit to set in those temperatures, but the fruit are frequently misshapen.

At temps above 96, lycopene (the pigment in red tomatoes) cannot form, so fruit of red-fruited varieties cannot ripen.

If the soil temps are above 90, the roots have major problems.

Cherries and small-fruited types seem to perform better in high temps.

At temps below 60, the plant is too cold for growth to occur.

Humidity and greenhouse varieties I can't help with.

Be sure to use a fan that will reach all the vines -- or manually shake them every day -- to ensure pollination; still air is a problem unless you have insects to pollinate or shake the blossoms.