The best time of day to plant your new vegetable starts, or any other container-grown plants, is after sundown, when the temperature has decreased a bit and the sunlight is not direct. Avoid planting in windy conditions, which can desiccate the fragile plant. If you plant in the evening, plants will have all night and early morning to make some adjustment to their new homes.
We have found that applying mycorrhizae to the roots while planting vastly improves a plant’s ability to adapt successfully. You can use either a granular or water-soluble form.
Be sure to give your new plants a deep watering and check on their water needs every day for the first week, then every 2-3 days in the second week. We also like to use Super Thrive Vitamin Solution in the first watering to minimize transplant shock. Compost Tea will activate the soil biology to help new plants access nutrients more quickly.
And, a foliar spray application of liquid kelp solution will strengthen the cuticle (‘skin’) of the leaves and stems and reduce transpiration.
In very hot, sunny conditions, it can also help a lot to erect some kind of temporary shade that can be left in place until the transplant has had time to establish its root system (about 2 weeks). An example are the below frames with screen material stretched over them and lashed to tomato cages at the corners, do the job of shading pepper plants and protecting the crops from hail, too. Use your creativity to come up with attractive and functional temporarily ways to protect your new plantings!
Applying a thick mulch will help keep plant roots cooler, and placing a landscape flag next to a new plant also helps you to keep an eye on it and remember to water.