How fast would a hypothetical spacecraft need to get to experience significant heating from interaction with the interstellar medium (ISM)? Significant, in this context, means a steady-state temperature (that at which radiative cooling balances the heat being generated) of a few hundred K or more. I am considering both the ISM and blueshifted photons here.
The means by which a spacecraft could reach such speeds are immaterial, or if it can be done at all, are irrelevant to this question.
An ideal answer will include a formula from which the temperature can be calculated for any velocity.