Answer: Impatiens are tropical plants and do not mind heat as long as they have enough water. They also do better in shade or morning sun. Based on your description it sounds like they are stressed and severely stressed plants will not bloom.
If they are in pots, move them to a spot in morning sun if you can, and be sure to water them thoroughly each time you water so that the soil is soaked through. Do not allow the soil to dry out between waterings -- you may need to water every day. Then apply fertilizer according to the label instructions. (Remember that too much fertilizer can damage plants.) You might consider using a blossom booster type (with a higher middle number) once the plants begin to recover a bit.
If your plants are in the ground, you will have a harder time of it. Shade them if possible. In any case, water them deeply rather than applying a more frequent light sprinkling. (The rule is an inch at a time, quite a lot.) This will encourage the roots to reach down deeper to where the soil stays moist longer. Dig down to see how far the water has penetrated -- you may be surprised. Again, do not allow them to dry out. You may need to water twice a week while the weather is hot and dry. Be sure the plants are mulched with several inches of organic mulch to help keep the soil cool and moist. Again, fertilize according to the label instructions as noted above.
Good luck with your plants!
Q&A Library Searching Tips