battery fan on when battery temperature < 80 F, and big red triangle waring on

Read codes first battery voltage off in blocks more than likely.

 

The traction battery that you installed is bad. I hope you have a warranty. The Dr.Prius screenshot that you posted shows a 0.43v voltage difference between the highest block and the lowest block. That is too high and likely triggered a P0A80 trouble code. You need to read the trouble codes to verify.

What traction battery did you install?

 

I dealt with the same problem with the battery in a Prius I bought with 305k miles on it. I decided not to play with the battery and replaced it with another one.
The problem may lie in the internal resistance of the module(s). As soon as the temperature of the modules reaches ~80 degrees, the computer begins to take into account the internal resistance. This can be seen in Dr. Prius app. 19 milliohms change to higher values. On my battery, delta SOC also began to increase as soon as the internal resistance values began to update.
This battery needs to be repaired if possible at all.

 

Dr Prius can't always pull codes from the hybrid control and HV battery ecu's.

Here's a thread that reviews some more capable scantool apps and devices.

The voltage for block 7 is too high compared to all the others, you have a problem with that refurb HV battery.

https://priuschat.com/index.php?posts/3290690

Posted via the PriusChat mobile app.

 

And how do you know your fans on You hear it running If you're hearing it running that means it's on full tilt too I have batteries out of these cars quite a bit and a lot of times when I'm working on them and messing around with him I leave all the interior out of the trunk area that I've taken out to swap batteries and play around I leave the fan and the duct work all plugged up and I noticed that I see the fan running on a real low speed quite often when the batteries not even warm yet. I'm not sure why that is nor do I really care because it's running so slow it wouldn't make any difference to anything I don't think and then when it's warmer here in North Carolina it gets into the hundred degrees no problem I don't notice my fan running any heavier or louder than it was in the spring or when it was cooler out It just doesn't seem to anyway of course I can't hear it until it's pretty much on full tilt especially if the car is moving If it's sitting still and there's not too much traffic noise you can hear it turn down the radio etc I'm not sure what 80° would have much to do with anything That's not even human body temperature yet I mean that shouldn't mean much of anything everything will be 80° standing in North Carolina in mid spring.

 

The fan turns on at higher speed when the battery failure occurs.

 

The battery cooling fan turns on the highest speed when certain hybrid battery trouble codes are triggered like P0A80. The first thing to do is read all the trouble codes using a Prius compatible scanner. See post #5.

 

I meant that the battery cooling fan turns on the highest speed when the triangle lights up with other lights on the dash because of the problem in the battery pack. When the fan is running on its highest speed, this is an indicator that the problem is in the hybrid battery and not with other components of the hybrid system.
What will it give you if you see the code(s)? Most likely the code will be P0A80, since the screenshot shows that there are at least 2 weak modules in the battery. The main problem is that the code appears when the battery pack modules reach 80 degrees, and i believe that replacing those two modules will not fix the P0A80 code appearing at 80 degrees.