Did you actually measured your temperature and see any fluctuation?
Some condition might mimic a fever like an hormonal issues in the morning due to diurnal cycling of hormone.
When we are asleep we are more likely to produce some hormones that requires the system to be less solicited therefore increased production during the night.
The symptoms can mimic a cold or a flu upon awakening that will disappear at some point during the day. Symptoms may persist longer.
The adrenal glands are responsible for the release of an hormone called cortisol (the stress hormone) and it follows a diurnal cycle too and is at it's max in the morning when you wake up therefore some symptoms can be observed. Several factors will affect your ACTH (adrenal corticotrophic hormone) levels such as stress, depression, temperature...
Supplementing with magnesium and Omega-3 and various other herbs such as calming herbs are good at reducing cortisol levels while caffeine and other stimulants and sleep deprivation will increase it. Basically you want to avoid stimulants before getting to bed for some obvious reasons other than that too but also you should take magnesium and calming herbs at night.
The use of medication/remedies can have an impact on the diurnal cycling of hormones.
Do not combine herbs, supplements and/or medications without knowing if there are interactions.
M4
I am not sure why that would be, most folks, if they are going to have a fever, have it night due to the fact their bodies are tired and run down more than they are in the morning. I could not find anything on google to explain this either as they say the same thing as I did. I would ask a health professional, maybe they can shed some light on this. Let us know what you find out.