The body temperature for an Arabian horse is the exact same as it is for any other horse breed 99-101.5 degrees Fahrenheit.
If you were asking about the horseman's term of classing a horse based on it's origins and overall type an Arabian would be considered a 'hotblood'.
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The Arabian is the most popular horse breed, followed closely by the Quarter Horse.
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The horse could be registered as a 1/2 Arab with the Arabian Horse Association. If the parents are approved for "warmblood" registration, the foal could be eligible.
The breed Arabian is meant to be a horse, but the breed does not determine this factor. If your horse or pony is or is under 14.2 it is a pony. 15.0 hands and above is a ahorse.
The cross of these two breeds is just a cross until it's registered as foundation stock with the Pintabian horse registry.