Substituting yogurt for cream without splitting the sauce

I'm trying to make a lighter creamy sauce using plain yogurt instead of heavy cream. The first attempt curdled into grainy bits when I stirred it into a hot pan. It still tasted fine, but looked terrible. Should I take the pan off heat, temper the yogurt with warm sauce first, or use a higher-fat yogurt? I'm looking for a weeknight method, not a perfectly stable restaurant emulsion.