  We prove strong unique continuation property for the differential inequality
$|(\partial_t +\Delta)u(x,t)|\le V(x,t)|u(x,t)|$ with $V$ contained in weak
spaces. In particular, we establish the strong unique continuation property for
$V\in L^\infty_t L^{d/2,\infty}_x$, which has been left open since the works of
Escauriaza [6] and Escauriaza-Vega [8]. Our results are consequences of the
Carleman estimates for the heat operator in the Lorentz spaces.
