As a GP I'm constantly surprised when parents bring a child to see me with "a high temperature" that they haven't actually bothered to measured. Yes, of course I then measure it, but a record of what the pattern of fever has been is invaluable; you know whether or not it is responding to treatment etc.
We did a study in our surgery recently involving, among other things, parents' reports of children's illnesses. We found that of those reporting "a fever", 60% HAD actually measured it (and so knew what they were talking about). Of the 40% that had not, only a tiny proportion (about 5%) of the children DID actually have a raised temperature when measured (allowing for medication given before temp was measured).
Other studies have shown that 'measuring' temperature based on feeling the child with your hand is ridiculously inaccurate; "fever" can be imitated by prolonged crying, and sweating, for example, when there is no actual rise in core temperature.
IMO a thermometer is a basic essential of family self-care, like having plasters and paracetamol at home. They are easy to use, and accurate (if using an aural thermometer). Forehead and armpit thermometers are almost useless, oral ones are usually OK, but often hard to use with children.