Why didn't my lemon tart set?
An analogue thermometer isn't too accurate. Besides, it sounds like you measured the oven temperature, not the tart filling. So I suspect that it was the heat after all. 

A custard with both eggs and starch needs to be thoroughly cooked. The reason is that yolks contain an enzyme which liquidifies starch. It doesn't happen outright, but will happen while your tart is cooling. The only way to prevent it is to heat the mix high enough so the enzyme is deactivated. 

To quote On Food And Cooking, 


  However, the survival of yolk amylase can spell disaster in the fillings for American cream pies, which are often made in the fashion of a bouillie rather than a pastry cream, and are held for hours or days before serving, enough time for a perfect cream pie to disintegrate into a soupy mess. No matter what a recipe may say, always be sure that the egg yolks in a starch-filled pie filling are heated all the way to the boil.