Mosquito bites, by themselves, should not cause fever. Bites become "inflamed" commonly (not infected) and can be red and a bit swollen, but again no fever. True "infection" is quite uncommon.
That said, mosquitoes, in certain parts of the world, can transmit all kinds of infections which can cause fever: malaria
, dengue fever
, yellow fever
, are all spread by the bite of an infected mosquito.