Well if you are display the image to your website user(s), theres not much you can do. Since you’ll operate identically to how the follow or channel pages work on the website. So you can’t exactly put a rate limiter in place and caching them on your own website, is generally, counter productive.
people if showing a users avatar, will often cache the user object and load the user object and show the iamge from that object for 24 hours (not the image but the URL to the image). But for a stream, the thumbnail_url doesn’t (usually) change for a stream. So your will also have browser caching.
You’ll only need to “defeat” caching when showing the image in other programs such as Discord. Otherwise, just use the TwitchCDN.