Low Body Temp/ Screening for Infectious Disease

Do people that normally have low body temperature get the same temperatures when sick with from an infectious disease as people who have a more normal body temperature? Also, would someone with a normal body temp of 98.6 or higher get something like Ebola? Just wondering if screening using body temperature as a fool proof way of detecting Ebola? For example, say someone who’s body temp is in the 96 degree range and they get sick with ebola, would their temp still rise to the same degree that indicates a fever as someone whose temp is around 98 to 99. That would mean their temperature would have to increase more than someone with a normal temp who gets a fever. Hope this makes sense.