By means of Monte Carlo simulations we investigate the finite temperature SU(2) lattice Higgs model with a doublet scalar field at large but finite quartic self-coupling. The lattices are asymmetric in space and time extensions and their spatial size is varied in order to study finite size effects. The second order deconfinement transition at high temperature of the pure SU(2) gauge theory changes into a crossover when the scalar field is coupled to the gauge field. The Higgs phase transition at zero temperature also changes into a crossover when the temperature gets high enough. Its position shifts slightly to larger values of the hopping parameter. This means that in the Higgs region of the phase diagram the system passes through this crossover when the temperature is raised at fixed values of the coupling parameters, in analogy to the symmetry restoring transition of Kirzhnits, Linde and Weinberg in the standard model.