TrainFan475

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Yes

Yes

I attempted to ask my husband what his other girlfriends and/or wifes think, but he promptly pleaded the fifth amendment, followed by dashing through the window and running away, so the results are inconclusive for now.

Been running bare for years, no issues so far

Just upgraded to high sierra and it's running like butter. I installed macs fan control and it took care of the fans running at full speed.

I hope you're planning to upgrade that to High Sierra. Lion is way out of date. Glad to hear that it's running though!

If you can do that and take a blank flash drive with you then that would make this a whole lot easier. 

I'm not even sure macs supported installing the OS from USB back then? Might have no choice but to use a DVD

My recollection is that without the thermal sensor adapter, the iMac ramps up the fans to 100% and I don't think an app can override their speed in that case. However, that may not be correct. It has been quite awhile since I read anything about it.
 
-KeithP

No that's the point, the fan gets set at 100% at the hardware level overriding anything an app could do. 
People wouldn't have bothered building custom caddies with the sensor if an app could solve the issue.

Yes. Macs Fan Control works perfectly for this.
Only the HDD fan is affected, and even then it doesn't always go up to 100%. However, it can be adjusted with Macs Fan Control for free. 
The fan is completely controllable in software - no sensor required. The replacement sensor method is more of a formality. 

Ah yes that dreaded series... If I remember well it will work without but the fan will be running at 100% continuously.

I believe those iMacs used Apple's funky thermal sensor with the installed HDD. I think you will need to get an adapter to make it work with an SSD. I noticed on OWC's upgrade page they list a thermal sensor as being included.
 
-kp

You should be able to unoffically run 10.15 or 11 just fine also with some tweaks. http://dosdude1.com/catalina/
 
One big thing is put a ssd in if possible, will make them so much faster.

Early 2009 apparently only comes with a Core 2 Duo, so seeing that you have an i5 it should be the late 2009 model.
Identify your iMac model
Specs for late 2009:     iMac (27-inch, Late 2009) - Technical Specifications

Is it early 2009 or late 2009?
 
Early 2009 can do 10.11 (El Capitan), late 2009 can do 10.13 (High Sierra)

It will support El Capitan without a doubt, and might support High Sierra.
I would make an El Capitan bootable USB and then update it if you can.

Or an original Mac OS DVD of a supported version.

Do you have another mac? Your gonna need one to make a bootable usb to install osx. 
 
here is the guide from apple https://support.apple.com/en-us/HT201372

I finally got my dream locomotive in HO scale! It's super hard to find because only one company produced it and it was a limited edition
 

I dislike all seafood, fish and what not, equally.
Literally makes me puke if it comes in contact with the inside of my mouth, can't even swallow.
My preference is for them to stay in the water so I never have to smell them.

Last I checked having weird dreams was a normal part of life