No, there isn't. It all depends on the regime.
If you are still talking about your supersonic rocket, for the nose cone, you can make an estimate like so:
[tex]T_{eff} = \sqrt{T^2 + \left(\frac{m V^2}{k_B}\right)^2}[/tex]
T is ambient temperature, T
_{eff} is the effective temperature experienced by the nose cone, V is the velocity of the rocket relative to air, m is the "average" mass of air particle, and k
_{B} is the Boltzman's constant.
Yes, they don't really add quite like that, but I don't think you need an exact number. For an estimate, this will do.
Keep in mind that only the very tip of your nose cone should be exposed to that.
Quote by rcgldr
I'm not aware of anything simple that is accurate. The mathematical models are usually empirical (based on actual experiements) and complex. It's a combination of friction and compression. At hypersonic speeds, it's mostly due to compression.

That's usually the worst in transonic regime. An estimate from simple ballistics is all he really needs. Not that it's going to account for nearly everything, but he's not building a jet fighter.