There is a related question here, which was more specific in only covering broth/stock at high temperatures, held indefinitely.
As stated in the question (and in my answer to the linked question, with another source), the usual cutoff is around 60C/140F. Just keep food above that temperature. Very few bacteria (or other dangerous microorganisms) can survive above that temperature for long, and if they are present, they will die off.
(That said, please monitor and verify that the food always stays above that temperature. Bacterial spores can survive above that temperature, and if you start dipping below 60C/140F for significant periods, you could grow nasty things. This is part of the reason why many government inspectors are so concerned about buffets -- something that's quite warm, but not steaming hot, is potentially a worse food safety hazard than something like leaving food sit out at room temperature, due to the elevated bacterial growth that often happens above room temperature.)
As noted in some of the comments, the practical limit is until the quality of the food degrades. High temperatures will tend to dry food out (if not sealed completely) and will gradually degrade some flavor components. Textures will also gradually break down, which make also make the food less desirable. (Just about anything that has any moisture will eventually become soft and mushy.)