Any fever reported by parents should be taken seriously, even without objective evidence.
There does not seem to be a consensus definition of fever in the literature. Most scientific papers for which a specific value is required to define fever suggest any temperature >38°C. However, the NICE guidelines on feverish illness in children define fever as 'an elevation of body temperature above the normal daily variation'.
This is often an important consideration in children with complex neuro development problems whose 'normal' temperature may be 35°-36° (be guided by the parents / carers) and in neonates when smaller temperature rises (e.g. 37.8°) are much more significant.