In a few days we expect two days with temperature about 95 and then it drops to high 80s. I understand it is not good for tomatoes. I have a dozen of 12 gallon pots. Should I bring them indoor or two days will not have effect on them? Why high temperature is not good for them, how it will effect them?
The plants are about 12-24" on average and some have flowers and some not yet.

I think it will effect the fruit set...but I don't think 2 days is going to be of any consequence. I can't bring mine inside so I'm not going to worry about it.

Yeah, it's pollination that is most affected by heat. They are fine outside.

I would shade them using anything to create shade like a tea shirt. You don’t need fancy shade cloth. I put any type of fabric I can find over the top of the cage. It helps a lot in a sudden heat wave. Actually after planting out my tomatoes I cover all cages with a mosquito netting or sun block fabric for at least two weeks to help acclimate them. We always get these crazy high heat days right around planting time. Even without the high temps the sun can be very intense for the smaller seedlings till they acclimate. Not planting mine here in NE PA till after the two day heat wave this weekend and closer to Memorial Day. Got caught last year planting too soon. It got very cold.

The problem with high temperatures is that it kills the tomato pollen. You may see a few blossoms drop after a heat wave, but the plants will be fine, they'll continue to flower and set fruit when conditions are right. I lose a few to heat every year, it seems inevitable that some days will overheat.
Shade and breezes help to reduce the temperature around the flowers.
You may notice as the plants get bigger, they develop their leaves and suckers as a means of shading their own flowers when it's too hot or covering them when cold. Also they behave as a community, and a plant that has leaves near another plant's flowers will shade them if they're close together. This is really noticeable in my greenhouse where spacing is tight and we get frequent extremes of hot and cold. So you may want to think about that when you decide how to prune your plants, and how to space them. I read yesterday that the forecasters are calling for a very hot summer in the NE States. Good luck!

They stop growing in Texas and disease sets in.
Might as well pull them here and plant okra.

The plants should be fine although if the pots are in the direct sun they may dry out quicker and need an extra watering.

Thank you all for insights! Let me recap what I learnt: 1. High temperature will kill pollen on existing flowers but will not affect the future flowers. 2. The plant will be fine but has a risk of getting blight and other diseases. 3. The plant itself may grow faster.
Did I got it right? If so then I see the next strategy: The flowering plants will benefit of bringing inside for 2 days. The seedlings which are not at blossom should stay outside to facilitate growth.
Is there a red line which I need to watch? The first day we are expecting 94 and the next day is 90.

You can surely bring in your flowering plants for a couple days--but what are you going to do when it's summer and it's 90+ for a week?

I usually don't have problems with tomato blossoms in the lower 90s - it's when it gets into the upper 90s for several days, when many drop their blossoms. The ones that have already set fruits, have no problems, it's when they start flowering again, the larger ones will take quite a while to ripen. This is why I grow so many smaller varieties, as they recover quickly, and start ripening quickly. But, of course, this area isn't as hot as others, though we are getting more heat waves than before. And fortunately, the humidity isn't as bad as in some areas, though it sure seems bad sometimes!

I worry about the roots getting hot in black containers. I shade some of my containers by leaning white floor tile against them.

Setec Astronomy wrote: ↑Thu May 19, 2022 6:34 pm You can surely bring in your flowering plants for a couple days--but what are you going to do when it's summer and it's 90+ for a week?

The plan was to bring inside for one day and then enjoy next month predicted temperature in the high 70s. Last year I overstretched myself getting between 40 to 50 plants and considering the fact that I had very limited time to care about them they were pretty miserable. For this reason I decided to limit this year to 8 plants but to invest my time to make them happy.

The weather guys improved the data and now they say that we should get 93 degrees tomorrow and 90 next day; then we go back to low 70s. I think that one day of 93 should not kill the flowers and I am contemplating on not undertaking the pot transportation back and forth (despite it is just few yards from the deck to the kitchen).

What is really hot for tomatoes? Does variety matters? I have Sungolds, Cherokee Purple, black cherry and black krym to worry about (they have flowers).

@Barmaley , one or two days in the 90's won't affect the plants top much, you may loose the odd flower, but nothing really noticeable. I have had plants survive days of 110F without a lot of damage as long as they have moving air around them. Still air at those temperatures is a different story, will cook plants

If I recall correctly, 95F is reported to be the pollen killing threshhold.