Answer: There are two distinct growing seasons in the low desert, a cool and a warm season, with different annual vegetables, herbs and flowers thriving in each. The cool planting season starts around late September-early October with plants growing through April/May, finishing their lifecycle as the heat hits. The warm season planting starts in Feb/March and plants thrive until the heat and some go through the summer with proper care. A good reference book that contains planting calendars for the low desert is called "Desert Gardening for Beginners: How to Grow Vegetables, Flowers and Herbs in an Arid Climate." ISBN 0-9651987-2-3
Parsley is a cool season herb. It won't survive outdoors much longer with temperatures rising. Basil and tomatoes are warm-season plants. They are usually transplanted outdoors from mid-February to mid-March to get a jumpstart on the season. They need to establish roots before intense heat. Tomato pollen isn't viable much over 90 degrees, so fruits won't set. The goal is to get tomatoes established, flowering and setting fruit before then. Some gardeners keep their tomato plants going through the summer and they may put on another crop later in fall. In June, cover tomato plants with at least 50 percent shade cloth, mulch them heavily to maintain soil moisture and cool soil temperatures for the roots.
It wasn't clear to me if they were all in the same pot. The basil and parsley can be grown indoors in a bright sunny window. Tomatoes need 6-8 hours of full sun daily to produce. The plants tend to get a little unwieldly for indoors. It depends on your space. Good luck!
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