We study the blow-up rate for solutions of the subcritical semilinear heat equation. We prove type I estimates for sign-changing solutions in possibly non-convex domains, extending previous results that required convexity or positivity assumptions. The proof uses the Giga-Kohn energy together with a geometric inequality controlling the effect of non-convexity. This is based on joint work with Hideyuki Miura and Jin Takahashi.