Is it possible to have an accurate speaker

I don't know. How do you define accurate? How do others define accurate? What conditions would have to exist in order for one to know what accurate actually sounds like? Maybe 'warm' actually is accurate. Don't know.

Accurate means low distortion. No argument on that as a definition. This is one area of speaker performance where we have seen measurable progress in the last few years, due to driver, crossover and cabinet technology.

Regards,

My definition of"warm" is like a warm body, meaning "lifelike"!

"Cold" is the opposite of warm and not lifelike.

Accurate is therefore always "warm".

I think the point of any good speaker is to reproduce whatever is put into it. If it always sounds "round" or "warm" regardless of the source it can't be particularly accurate as, after all, music tonality is nearly infinitely variable. Or something.

Accurate usually means "true to the original" the original being whatever is fed to it as noted above.

OTOH, "warm" can be one or more of many things: a BBC type downward sloping speaker response curve, linear or non-linear distortion, muted high frequencies, augmented mid-bass frequencies, over-damped listening room, blown tweeter ;), a recording without strident highs, a well-balanced recording, lack of sibilance and very extended high frequencies...