Yes, when a woman is pregnant, her temperature should remain high which is because of the hormone changes in her body. Once the temperature drops, very likely a miscarriage will happen or something wrong with the pregnancy that cause the drop of pregnancy hormone.
It varies from person to person. If you have been taking your basal body temperature everyday, you should see a temperature shift after ovulation. If you are pregnant, your body temperature should remain about the same temperature or higher as after ovulation.