What's "central heating"? I believe Germany already uses central heating in most places. The question is what powers it. Can it be efficiently replaced by renewable-energy (!) electric heating vs. fossil? Other commenters have posited "no".
The way I see it, investing in nuclear should have been part of the plan, instead of replacing it with renewables (vs. doing so for those uses of fossil where renewables make sense). The fear of nuclear energy in Germany is just ridiculous IMO, and arguably has become a self-fulfilling prophecy. With nuclear power on its way out know how and effort to research and to maintain existing plants and investment in it are at a minimum making continued operation now a liability.