  We produce a finite time blow-up solution for nonlinear fractional heat
equation ($\partial_t u + (-\Delta)^{\beta/2}u=u^k$) in modulation and Fourier
amalgam spaces on the torus $\mathbb T^d$ and the Euclidean space $\mathbb
R^d.$ This complements several known local and small data global well-posedness
results in modulation spaces on $\mathbb R^d.$ Our method of proof rely on the
formal solution of the equation. This method should be further applied to other
non-linear evolution equations.
