Curly hair does not mind in high heat, giving you the freedom to use irons that do not have adjustable temperature settings. However, if you can choose between different heat levels, this is a function that you want to use. Also, curly hair is usually healthy, so you should not consider units that cannot reach at least 400F of heat.
If you choose a straightener for thick hair, you can go with a high temperature between 400-450F. But if your curls are not that aggressive, and you would describe your hair as beautiful and sensitive, you can go with a lower heat content.
You may need to experiment to see how your hair reacts to different temperatures. In that case, always start with the lowest setting that you think will work to straighten your hair.