Only take the temperature of adult chickens, not baby chicks. If your chicken seems ill and you want to check her temperature, you can do it by yourself, but it's really much easier with assistance: one person can hold your hen still, while the other can use the thermometer. Please get assistance if possible. An assistant has two hands to restrain your chicken safely, while you have a better angle to see what you're doing.
If you're by yourself, in order to take your chicken's temperature, you'll need to restrain her with one arm. You want her bottom facing forward. Her wings should be held to her sides between your arm and your body, and her legs should be held with your hand. When she is restrained, insert a lubricated rectal thermometer into her cloaca with your other hand. Just an inch or so is far enough. Do be sure she's firmly but gently restrained, because if she starts struggling she could break the thermometer or really hurt herself!