thermostat, or water pump are the most likely causes... try the thermostat first... that is the cheapest and easiest one... if that doesn't solve the problem, you've narrowed it down to the water pump
Could be a hole in a hose, a heater hose, the water pump could be leaking, there could be a hole in the radiator. Many times condensation from the AC evaporator is mistaken for a coolant leak.
Check the Battery and cables and if it's not that it could be the alternator.
it could be the themostat housing gasket
Could be many answers to this problem. Starting with worse-case and going to best case scenario... Check coolant level. If you've serviced the coolant regularly and coolant is an off-color or is contaminated, then run a compression test. If the level is low, it could be an internal engine leak or external leak. (hopefully external) If coolant checks-out, then try replacing the thermostat. Sometimes the gauges will read incorrectly and so that's another possibility.
Could be the sensor that has gone bad if the coolant level is correct. Find a trustworthy mechanic to check that out.
by "burning coolant" do you mean that there is the smell of burning coolant? or do you mean that your coolant level is constantly needing to be topped off and you don't know where it is going? if you smell burning coolant you have a leak somewhere and its probably dripping onto the exhaust. you need to find the leak. if you are constantly leveling off and there is no coolant leaking under the vehicle it could be a blown head gasket. check your oil for coolant contamination. pull the dip stick and check the color of the oil: dark, almost black in color=good; lite creamy brown (like creamy coffee) =blown head gasket. or it could be a blown intake manifold gasket instead of head gasket. 1996 silverado has a two piece intake manifold, an upper and lower intake manifold.
check coolant level check thermostat may be stuck closed
The new sensor could be stuck. Or the wiring could be loose, or the coolant could actually be low. Check the coolant level and the sensor wiring first.
it is low coolant temperature, could be the thermostat could be the sensor for coolant temperature.
Check coolant level Could be alternator going bad Could be coolant fan going bad
it could be your emission check sensor
It could be symptomatic of a larger problem. The coolant may not be circulating properly, or the indicator panel or car's computer could be developing trouble.