Generalizing work of Polya, de Bruijn and Newman, we allow the backward heat equation to deform the zeros of quadratic Dirichlet $L$-functions. There is a real constant $\Lambda_{Kr}$ (generalizing the de Bruijn-Newman constant $\Lambda$) such that for time $t\ge\Lambda_{Kr}$ all such $L$-functions have all their zeros on the critical line; for time $t<\Lambda_{Kr}$ there exist zeros off the line. Under GRH, $\Lambda_{Kr}\le 0$; we make the complementary conjecture $0\le \Lambda_{Kr}$. Following the work of Csordas \emph{et. al}. on Lehmer pairs of Riemann zeros, we use low-lying zeros of quadratic Dirichlet $L$-functions to show that $-1.13\cdot 10^{-7}<\Lambda_{Kr}$. In the last section we develop a precise definition of a Low discriminant which is motivated by considerations of random matrix theory. The existence of infinitely many Low discriminants would imply $0\le \Lambda_{Kr}$.