Why 2005 es330 just had alternator repaced now a/c is not blewing cold all the time goes hot then cool but not cold after driving

Question edited for clarity.
Question moved to model category.

I have the same year and model Lexus. I bought it in 2007. Great car.

Wiring diagram in the link. It should have come complete, remove the old and install / connect the new one.

https://www.google.com/search?q=2005+lexus+es330+alternator+wiring+diagram

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catalytic converter stoped up or tailpipe pluged

check coolant level could be too low allowing air in the cooling system causing air pocket in engine around the engine coolant sensor.coolant sensor needs to be in hot coolant so it will cause the cooling fan to come on at a set temperature.make sure coolant correct level and the coolant level in the cooling overflow jug should be at full cold mark.the cooling overflow jug should never be empty,if you see empty cooling overflow jug air got in the cooling system so make sure when engine cold every time raise hood make sure cooling overflow jug coolant level at full cold mark.if jug stay empty you have cooling leak.so replace radiator cap,if coolant level all good,i would replace the engine coolant temperature and thermostat.when your car come to a long stop or driving along long line of slow moving traffic the engine coolant blower motor should running if not have vechicle code scan for faulty coolant fan motor control module.or ecm problems.

The diagram is a little hard to follow, but it looks like on the high fan relay there are 5 circuits like on the hi-low relay.
Pin 86 is power for the magnet, 85 is the ground signal from the module. The module grounds the magnet to move the contacts.
Pin 30 goes to the fan and pin 87 goes to a 50amp fuse.
Pin 87A is a jumper between the two relays.
The fan motor gets power from three different sources and is grounded to the car. The other two wires are return signals to the module. Kind of like a three way light switch in a house.
On the fan control relay, pins 30 and 85 are hot, pin 87 goes to the fan motor, and pin 86 is grounded by the module.
I can send you the diagram in a separate message if you need to see it.

2 possible things. 1st(cheapest) you have air in cooling system. Need to burp it. 2nd(expensive) you may have blown head gasket. I tend to think air is in cooling system and your level is low.

I had the same problem due to a bad battery. When I replaced the battery the same issue with heat on passager side and cool on the drivers side. After turning the engine off and back on five times the computor reset it's self and both sides blew cool.

If air is hot then cold it sounds like you have a sizable air pocket in the cooling system. This could be caused by a leak or if you have recently done anything to the system without bleeding it afterward.

Start by flushing your coolant system, then refill with a quality coolant.
Run up to temperature and check again for level (when cool again)

Check that the radiator is getting really hot quite suddenly when running from cold, as this is the best way of checking thermostat operation.
When over a set temperature (check your manual) the fan should come on.
If it never does - troubleshoot the fan (temperature switch or sensor first, then fan on direct feed to see if it powers up ok)

could be the temp sensor for the coloing fan you have 2 one for the ecu and one for the fan

sounds to me like the thermostat may be stuck. i would check the coolant, fan, and belts.