Does Mail for Exchange for S40 automatically adjust the Heartbeat value based on server HTTPS responses?

No, Mail for Exchange for Asha 302 and 303 devices does not auto adjust the heartbeat itself. You will need to set this manually if the application keeps dropping the connection in a particular network. The problem is often characterized by the application constantly requesting for a new connection or getting disconnected after an idle time. When changing the heartbeat setting, you should start with a smaller number than what is already set and keep reducing the number until it starts to work normally in that particular network. Having the value lower will impact the power usage directly. The goal is to set it as high as possible.

The default value is 15. You should not change the value except if you have problems with the connection.

You can find the heartbeat settings from Menu > Apps > Apps and Games > Mail for Exchange > Options > Settings > Schedule > Direct Push Heartbeat.