There are four relays that run the fans. Check them. In the mean time run your defogger and that should kick on the fans.
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If the smoke is coming from the exhaust then it's coolant. If its not turning over then it could be hydrolocked from a coolant leak.
You could have a partially blocked radiator or a thermostat that is not opening. If neither of THOSE are the problem, you could have a warped head that damaged the head gasket.
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.
The coolant leak is pretty cut and dry - you have a leak somewhere. The lukewarm heat (assuming you're referring to the car's heater) could be for a number of reasons. Insufficient coolant could be one of those. Your coolant could be burnt out. It could be a problem with one of your heater hoses. You could have a worn out heater core.
You could possibly have a circulation problem, or a over heating problem. Need more info.
First thing to do is check the coolant level.MAKE SURE THE ENGINE IS COLD BEFORE REMOVING THE RAD CAP.If the coolant level is low, it is most likely due to a leak.The thermostat might be sticking,or perhaps the electric cooling fan is not turning on when it is supposed to, it is controlled by the vehicle`s computer.Worst case scenario could be a faulty head gasket or a cracked cylinder head. I suppose it could be a circulation problem but I have found this to be rather rare,(water pump problem)
Intake manifold gasket
If a car engine stalls when turning, there could be a problem with the power steering pump. There could also be an issue with an emissions control device.
If it is an automatic transmission, the cooler in the radiator is most likely leaking into the coolant system.
A bad coolant temperature sensor is one thing that could cause an idling speed problem with a Peugeot 406. There could also be a problem with the idle control valve.
coolant tempure sensor,thermastat