When you log in with SSH, your client has the private key, and the server has the public key. Therefore, no vulnerability on the server can leak your private key, since the server doesn't have it.
The server cannot use Heartbleed to get the private key from your client, since that's an SSH implementation, and only OpenSSL SSL/TLS connections on version 1.0.1 to 1.0.1f are vulnerable. No other implementations of any type at all have this issue, including all SSH implementations.
Now, if the server has its own private SSH keys in memory somewhere, then deeper investigation would be called for.... but it would be cheaper to fix the vulnerability and then regenerate the server's SSH key pair, since there's no Certificate Authority to pay to sign SSH keys!