why is the body temperature of homeothermsslightly higher than the environment?

It is not always necessary that the body temperature of  homeotherms are higher than the environmental temperature.  Homeotherms can maintain a constant body temperature regardless of the environmental temperature, they do so by regulating the rate of their metabolism.  The temperature goes slightly higher because of the basal metabolic reaction occuring in the body.  In response to temperature fluctuations outside, the body increases or decreases the metabolic reactions, but some basic metabolic reactions are always occuring in the body, so the temperature goes slightly higher.