My first suggestion would be a loop of creating an LHA (archive) from files held in RAM: but without any means to get lha to the amiga ... I guess that's not a possibility.
Could you write a basic shell script to repetatively copy files in RAM:? Or - can you loop basic mathematics from the command line? I'm not sure what capabilities the CLI has ...
Also, I'm curious what heat difference there is under load for a 68030 CPU. How does the Amiga kernel 'idle'? Would doing useful work stress the CPU any more than the thing being sat in some sort of amiga kernel idle loop?