  We consider the semilinear heat equation with a superlinear power
nonlinearity in the Sobolev subcritical range. We construct a solution which
blows up in finite time only at the origin, with a completely new blow-up
profile, which is cross-shaped. Our method is general and extends to the
construction of other solutions blowing up only at the origin, with a large
variety of blow-up profiles, degenerate or not.
