In the short term your user is compromised whether it's a cookie, an AES key for the TLS session (which will presumably still have to be resident in the process sending you data), a credit card number in a POST request, or your certificate master key.
Anyone who can intercept my traffic in close to real time, and wishes to target me, is going to know I'm talking to amazon.com, IP x.y.z.f, and that that's where they should target their Heartbleed attack for a good stab at accessing my PHP session cookie or TLS session AES key.
There are some cases, like e-mail phishing, where this isn't the case of course... but then a redirection service would be sufficient to let me script an attack against many sites.