A very poor job of cleaning the compound off wouldn't account for it shutting down under load. I frequently don't bother changing the paste at all, doesn't seem to matter. Currently using a mix of mx2 and as5 for no good reason, temps are good regardless. People worry too much about pastes.
Whether the heatsink is hot or not is a very good question. If it's burning hot, contact is fine, and either the heatsink fan is doing badly or airflow is really poor. If it's cool to the touch while the cpu shuts down, contact is bad.
The only time I've seen temperatures like that was when I got a keyboard cable caught in the cpu fan and I didn't notice until it turned off. My guess is a faulty mounting bracket for the heatsink, if you bought retail it's well worth trying the stock hsf to see if the issue remains.