Something wrong with my ford

So I recently got a 2002 Ford focus wagon automatic ztw with 85k miles. Runs great except for when driving over 45mph after a couple minutes driving faster than 45mph the automatic transaxle/ cooling system light comes on and the speedometer starts acting a little weird an example is while going 65 it was bouncing between 62 and 67 mph it was showing (while in cruise control) and randomly it dropped to 50mph while the speed still definitely felt like 65 but the car just starts ramming into pull power as if it the car wasn’t recognizing its own speed. I’m not sure if the automatic transaxle/ cooling system light is causing this but I figured I’d put that the light goes on. Also when I get into towns and start driving under 45mph the light turns off and cruise control works fine no bouncing in mph in the speedometer.
Just wanted to know what could be affecting this.
Will be running down to a auto store soon to see if there’s a code.

how’s your transmission fluid level and what color/smell is it? when was the transmission fluid changed last?

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You may have just found out why the car was for sale!

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Sounds like the transmission output speed sensor is failing.

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That was my first thought too .

Checking for any codes is a good idea and I wouldn’t be surprised if the issue is tied to the speed sensor.

If the vehicle speed sensor fails that confuses the powertrain computer and can make the engine and transmission misbehave. Speed sensor failures which occur only at higher speeds are not that uncommon.

So I went and got my code read all that came up was a p0125 code.
Still having problems with my speedometer and my cruise control not working properly. Which sensor needs to be replaced for this to be fixed I noticed there were 3 kinds with this car the output the input and the input transaxle speed sensor, turbine shaft speed sensor. I’m guessing the transaxle input speed sensor due to the light coming on? Any input would be helpful. I have an automatic transmission for clarification.

P0125 is insufficient coolant temp. Bad thermostat or bad coolant sensor. Not a transmission sensor of any kind.

So is the car coming up to the proper temp quickly? If not, t-stat ismpretty likely but I’d change the coolant temp sensor since you drained out a bit of coolant.

Yeah I understood that it was a bad thermastat or bad coolant sensor. But that’s not my concern as my speedometer bounces back and forth when going 40mph or faster when using cruise control and my concern is about fixing my speed sensor, my question now is since no other codes came up which speed sensor do I buy in a attempt to fix my car randomly slamming on the gas while in cruise control and pushes my car an extra 20mph faster while the speedometer still shows the speed retaining the same speed.

I would say the output shaft speed sensor mounted on the automatic transmission

https://www.rockauto.com/en/moreinfo.php?pk=10052216&cc=1385557&jsn=544&jsn=544

Print that page out when you head to the auto parts store . . . it also lists Motorcraft part numbers, in case the parts guy wants to see them

As for P0125 . . . either your coolant level is low, and thus the coolant temperature isn’t getting an accurate reading, or you need a thermostat

If the coolant level is low, you’d better find out why . . .

the transmission input shaft rotates at the engine rpm. the transmission output shaft sensor rotates proportional to the vehicle speed. the turbo shaft sensor is used for the turbo and not directly related to the engine rpm or vehicle mph dash display.