On the direct connecting I totally agree with Matt_h. I even add that it would be wise to use the original Amiga keyboard (if still available and working).
I ran an un-modified A3640 in my A3000D/16 for a few years without any problem. It was also fitted with the DKB memory board with a PicassoIV with TV-tuner. Other heat-producers inside the case were two SCSI harddisks. What I did do when I got the DKB3128 was shifting the 1 MB FastRAM chips (located underneath the drive-area) to the ChipRAM area (located in the ZORRO III area). That took a little heat out of the drive-area.
When I fitted the A3640 (after the machine came from the shop that modified the main-board so it could use the 3640) I took it apart again to make sure the internal SCSI cables were as short as possible and routed in a way that allowed maximum air-flow from underneath the drive-bays towards the PSU.
To keep things as cool as possible make sure the floppy-drive is in its original position (right above the accelerator board). As it's less used than any harddisk it should remain cooler, alowing better heat radiation from the accelerator.
Another thing... Have you tried starting up the machine without all the extras? Might be a software issue.
