"pulling off the eeprom" -> No you won't  
There is no eeprom in the ecu!  Nowadays it's a flashrom, as of M3.83/M5.82.

Can't make any contact with the ecu at all ?  Had it problems before ? (dtc's)

Read sticker on ecu, and read-out software via obd or benchflashharness. Compare
numbers (look into the software) if they match with the sticker. Ifnot, you might have
found the problem

Normally they don't get that hot when doing nothing... Otherwise bosch had placed a heatsink
i think. They generally do a proper job on electronics as of design.

Cheers,

PvL