I have the replacement thermostat for a 2003 bmw 3251 2.5 in hand however i need a diagram or some advice how to get started

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Videos and diagrams

https://www.google.com/search?q=2003+BMW+540i.+Diagram+to+set+camshaft+timing

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some ideas
https://www.youtube.com/watch?v=vl7BkzQBgHY
https://www.youtube.com/watch?v=eY_zhq74_no
https://www.youtube.com/watch?v=mc-1rXGatHE

Tough to say without a fault code read out. There was a nice service information bulletin about your instrument lighting up like a christmas tree that lead to an engine harness. Your thermostat could also do that. As long as your check engine light NOT on and your coolant level is good, then you should be ok to drive on it. While a jammed thermostat will sometimes not set a fault, it could over heat your engine. With the vehicle COLD, try opening the expansion tank then starting the vehicle, if you see a small jet of coolant then your water pump is good.

Any major brand oil is ok, the type is 5W-30W or for hot climates 10W-30W

CLICK on the following LINK. It has the Belt Diagram you will need.

If you would: Before Clicking: Let me know if this helped you, or if you have any additional information or questions. Feel Free to contact me at FixYa.com!

http://www.2carpros.com/car_repair_information/year/2003/make/bmw/model/z4/2003_bmw_z4_drive_belt_routing_diagram.htm

The thermostat is inside a black plastic housing, It is inside the housing assembly where both radiator hoses meet up by the engine. You can't replace just the thermostat, the whole housing has to be replaced,

the dealer parts dept usually has the best exploded diagrams

I don't have a diagram for you however I do have some sound advice. If you have never changed out a window regulator, you don't want to start learning with a BMW. Believe me you will rip most of your hair out by the days end and you'll rip a lot of skin from your hands and arms. There are too numerous little tricks and rules to follow for me to list. Trust me when I say, bring it to your favorite mechanic, it doesn't have to be a dealer, but, you do not want to undertake this project.

Which lights, do you know what they are or can you describe them?

remove steering wheel (17mm hex nut)
remove screws from dash cluster(3 on bottom. 2 on top)
Unplug connections to cluster
Tilt towards you and pull up, and that it!
Trust me , you want to take the steering wheel off , makes the job much easier!