How to treat prickly heat on toddlers quickly?

Get the child in a shaded area and remove some of their clothing. Apply cool rags to the areas affected by the rash (I assume by prickly heat you mean heat rash), when you remove the rags don't rub them dry, let them air dry. Calamine lotion can be used but avoid any other anti itch creams as they can make it worse. As far as the visible sign of the rash it can't really be treated, but the symptoms can be dealt with to make your child more comfortable.

If the rash gets worse or your child seems to be in pain or severely itchy you probably need to see the doctor.

Oh also because it can get itchy, you might want to cut their fingernails so they don't dig into themselves and make it worse while scratching.