Which hose contains the Thermostat on 1998 Cadillac Deville with Northstar engine ( build date 12/97 )

The most common overheating problem with the Northstar engine is a blocked purge line(small hose).The purge line is designed to purge air out of the cooling system.
There is a small diameter hose coming from near the top of the coolant tank (not the cap) ,this is the purge line.
With the engine idling,pull the purge line from the tank,if there is no coolant flow from this small hose,it is blocked and this will cause overheating.
If the hose is clear, check for blockage at the nipple on the tank.Or trace the hose back until you find the blockage.
The hose goes in to the engine to a crossover and comes out the other side close to the thermostat housing,the blockage may be there.
If you still wish to replace the stat...
The thermostat in the northstar engine is located at the bottom radiator hose (unlike most conventional cooling systems), the hose connects into the housing where you will also find the water pump.

You will need to remove the air filter housing and air duct to gain easy access to the thermostat.

Remove the hose from the housing,then remove the two bolts on the flange,the thermostat can then be pulled out.

Take note of the orientation of the thermostat as you remove it.

The thermostat in the Northstar engine is a dual action device.
One end of the stem is the Thermostat(obviously) and at the other end is a spring loaded pressure valve(the thinner end).
Make sure the thermostat end is nearest the rubber hose and the pressure valve end is in towards the engine.

The normal operating temperature for the Northstar engine is around 210 degrees.
The fans will not come on until the temp hits 225 degrees.

The thermostat in the northstar engine is located at the bottom radiator hose (unlike most conventional cooling systems).

The most common overheating problem with the Northstar engine is a blocked purge line(small hose).The purge line is designed to purge air out of the cooling system.
There is a small diameter hose coming from near the top of the coolant tank (not the cap) ,this is the purge line.
With the engine idling,pull the purge line from the tank,if there is no coolant flow from this small hose,it is blocked and this will cause overheating.If the hose is clear, check for blockage at the nipple on the tank.Or trace the hose back until you find the blockage.The hose goes in to the engine to a crossover and comes out the other side to near the thermostat housing,the blockage may be there.

If the other end of your purge line is not connected to anything then that is the problem......it must be reconnected otherwise the cooling system is not pressurized.

The thermostat in the Northstar is in the lower hose as you have stated.
The thermostat in the Northstar engine is a duel action device.
One end of the stem is the Thermostat(obviously) and at the other end is a spring loaded pressure valve(the thinner end).
Make sure the thermostat end is nearest the rubber hose and the pressure valve end is in towards the engine.
The cooling system in the Northstar does not work like the older,conventional systems, this is why most people are confused when they find the Thermostat in the lower hose.

The most common overheating problem with the Northstar engine is a blocked purge line. It's job is to purge air out of the cooling system.
There is a small diameter hose coming from near the top of the coolant tank,this is the purge line.
With the engine idling,pull the purge line from the tank,if there is no coolant flow from this small hose,it is blocked and this will cause overheating.If the hose is clear, check for blockage at the nipple on the tank.Or trace the hose back until you find the blockage.The hose goes in to the engine to a crossover and comes out the other side to near the thermostat housing,the blockage may be there.

Assuming you have the Northstar engine....

The thermostat in the northstar engine is located at the bottom radiator hose (unlike most conventional cooling systems), the hose connects into the housing where you will also find the water pump.
Remove the hose from the housing,then remove the two bolts on the flange,the thermostat can then be pulled out.
Take note of the orientation of the thermostat as you remove it.
Don't forget the new gasket when you install your new stat.

No it has to be a 32 valve northstar engine

do the heater core coolant supply hoses both get hot at the firewall in the engine compartment? if yes then you have a defective temperature control blend door actuater motor.

Your engine is a 4.6 liter 281 CID V8.

There are thermostat rated for 180f or 195f for your engine,

I will select a 195f thermostat with a pressure relief poppet/valve to protect the coolant hoses.

Your car probably has the 4.6 northstar. If this is the case the thermostat is in the water pump housing at the drivers side of the engine. follow the lower rad hose to the pump housing and its contained in a black (2 bolt 10 mm) housing.