I have hopes for Rust, too, in this space. They're making a lot of good design decisions to balance safety & performance. Far as Heartbleed, that sort of thing can be detected using techniques from "information flow control security." Essentially, the programmer labels resources in terms of confidentiality and integrity. The type system, compiler, whatever checks them against a security policy. So, a variable containing confidential data shouldn't be accessed by functionality sending data to public sources.

Here's an example from one of the leading groups in the field:

http://www.cs.cornell.edu/jif/

That was turned into SIF, Swift, Fabric, and I think Civitas voting system. Swift even auto-partitions the system between client and server side while maintaining confidentiality/integrity policies. Fabric kicks butt on all kinds of issues in the hardest space of them all. So, given the above, I'm sure a problem like Heartbleed in a mere SSL protocol would be trivial to prevent at language level if software and compiler developers merely chose to adopt info-flow security at least for important projects.

Note: One can use stuff like that even if not supported in main tool set by creating a mock-up of software in supporting toolset. The abstraction gap presents issues but a problem in one might mean problem in other. Especially for what amounts to covert channel analysis of software.