It's normal for those devices be be fairly warm, approx 50°C. U3 (Paula) contains a UART responsible for serial data to and from the disk drive. The two CIAs, U7 & U8, handle the other digital I/O for the disk drive.
Depending on the exact problems you have, you can narrow it down to various hardware blocks. E.G. if you can read anything then the RX serial data is OK, but if you can never write to a disk, it could be a problem with the TX data or write enable line.
Personally I'd just swap U3, U7 and U8 for known good devices as it only takes a couple of minutes to do.
But assuming you don't have any SMD soldering equipment handy, you can't really do a lot other than check continuity of the two serial lines and the various I/O lines between the floppy port and the relevant pins of U3, U7 & U8.
Also check for shorts to ground or +5V on those lines, as that can indicate a short circuit output logic within U7/U8.
I have A1200 schematics here if you need them:
http://amiga.serveftp.net/schematics.html