The Claude (and ChatGPT) web UI supports incognito/temporary chats that are discarded when you close the tab. Click the ghost or dotted speech bubble icon in the upper right corner of the page.

I use this as my default mode so I don't clutter my chat history with random, one-off questions I ask. Unfortunately, there is no way to change your mind and save a productive incognito chat after you've started chatting.

I feel like every time I try to use this feature, I get burned because I accidentally use the back touchpad gesture, or I accidentally close the tab, etc. Or, I remember one time I was using the Claude iPhone app, and I quickly switched apps to respond to a text message. My phone must have been low on memory or something, because as soon as I switched back to Claude, the app faded to the startup screen and the whole conversation was gone.

Which of course is the entire point, so I don’t really know what I want here, but what they have right now isn’t that usable IMO. Maybe a chat that lasts 24 hours? And, it would be nice if there was a way to convert an incognito chat into a persistent chat.

the request still went to a server you have no control over.

For all we know these temporary chats are saved and linked to your account but just don’t show up in the UI.

I believe they are. In the case of my organization's account, Incognito chats are even visible to admins.

An interesting/odd way to think about the feature is that you're not hiding the chats from other humans, but from Claude.