Interesting question.Covid is the disease you develop after being infected with the Sars Cov 2 virus and a disease is diagnosed based on symptoms, now we know many people can test positive for Sars Cov 2 and not have any symptoms so those people would technically not be diagnosed as having Covid.If you don't have a temperature but display other symptoms and test positive for Sars Cov 2 then you could be classed as having Covid, so it seems to be possible to have Covid without an above normal temperature.