** Do not take this as Official HP Support **
If the drive shows up with temperature and all of the features, it is working as intended in the array. From what I can tell, you have the same info. as my other SSD's show in the DL360 G5 I have.
The DL380G5 is a PCIe 1.0 machine, and it will be very much bandwidth and performance limited. You will be limited to PCIe 1.0 x4 performance (10Gpbs), which is enough to run a few drives off of the internal card. To go to the 410i or others, you will need to get some adapter cables to transition the older SAS/backplane connectors to the Mini-SAS format. I know others have done this. But you will need to find those cables, which is not easy! You will be stuck at the 10Gpbs speed, with no real benefit in changing it over.
I would not replace the card for just temperature readings though. Officially, the P410i is not supported in the DL380G5, meaning, HP does not test or validate it will work. It also means that the 410i and the DL380G5 are a untested combo, and well, its buyer or tinkerer beware. That has not stopped me from hacking up a few machines, as it was/is a fun learning exercise.
My best advice on using the current P400 you have, it make sure you are fully patched to the latest and greatest BIOS, P400 and Disk Drive firmwares. I know the 7.22 firmware on the P400 works great with SSD's, just you do not get any TRIM support.
HTH!