95 Jetta sensor temperature light

What can cause a 95 Jetta's temperature sensos light to stay on? It seems to run fine but there is a hot/slightly burnt smell when you lift the hood.

had this same problem
the light would go on even when the car wasnt hot

my heater core blew up today
and i had to bypass it untill i can fix it
and i noticed after i bypassed my heater core, the temp light stoped going on

so there could be a clog in your heater core