Temperature what is the ideal temp the 98 deville should run at

aprox 215 to 220 deg. F. vehicle can run has high as 220F in a closed system. water boils at 212 F degs.
check for blown headgasket,look for exhaust gases in radiator jug. (will need CO tester) or blocked radiator.

Most GM vehicles run from 195-205.

I would suspect either the temp guage or the coolant temperature sensor being inaccurate. The new thermostat is probably working good, or else you wouldn't have a very warm heater. If you have electric radiator fans, you might check to see if they are running all th time. Electric cooling fans should only come on when the temperature sensor reaches a predetermined coolant temp, or when the a/c or defroster is turned on. If the fan runs all the time, the engine would not reach normal operating temperature.

Who did all this work?
Was the water pump bad?
Was the radiator, so clogged it could not be cleaned?

What diagnostics was done?

Is the car actually over heating? That is where you start

All that work may have been for not

When you removed the stat,the temp never went up,only the gauge,
can not run a veh without the stat, the temp sensor needs it in there

Is the exhaust converter partially blocked?
Is the engine running rich

Have the data looked at.

air sensor keeps fans at a constant temp.adrian,,,,,,,,,,,,,,

The temp. should stay within that range, but should never be allowed to run 0ver 240, if it does you have a problem

The standard thermostat temperature is 195 F.

The ideal running motor running temperature is between 195F to 210F.

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Are you having over heating problem.

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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.

Sounds like the theromstatic is sticking, making the temp to run higher than normal. The temp should be around 185 to 190 tops. Also check the flues on the radiator, make sure it is recirculation well once the theroms. open up. I not sur if this has a clutch fan or and elect.fan. But make sure it is pulling air thru the radiator well, to help to keep the motor cool.

Could be a few things but either way, don't wait to have the cooling system checked out, do it now & possibly save $1000's later.
Check your coolant level first, make sure all belts are there. Rad fan should be coming on when it reaches operating temperature etc. Just bought it from who, a dealer? If it was a dealer head back to him a.s.a.p. and give him a chance to make it right, and pay close attention to what he says it is/was.