An efficient way to study the QCD phase diagram at small finite density
is to extrapolate thermodynamical observables from imaginary chemical
potential. The phase diagram features a crossover line starting from the
transition temperature already determined at zero chemical potential. In
this talk we focus on the Taylor expansion of this line up to $\mu^4$
contributions. We present the continuum extrapolation of the crossover
temperature based on different observables at several lattice spacings.