The smell sense of the brain is very near the face and eyes. The article mentioned below doesn't discount fever is a symptom but the one characteristic that sets the SARS-CoV-2 apart from others is it's brain involvement.
After receiving smell information from the nose’s sensory receptors, the olfactory bulb relays the information to a circuit of brain regions for processing.
May 18, 2020
Now, a study from the Harvard-affiliated Cambridge Health Alliance (click here) that was published in Mayo Clinic Proceedings has examined 1,000 records from outpatients. The researchers were looking for differences between COVID-19 and other diseases that have similar common symptoms. What they found was that shortness of breath for COVID-19 patients gradually becomes worse over a few days, and that fever is not "a reliable indicator" for infection. The study also found that the disease can just start with coughing and no other symptoms at all....
...On top of that research, doctors from Europe examined 1,420 patients from 18 different hospitals, and what they found was that fever was only present in 45% of cases. The most common symptom out of all the patients was headaches at 70.3%, followed closely by a loss of smell at 70.2%....