Been here and bought the T-shirt mate
I had quite decent heatsinks on my LMD's but at 3.0A they could still kick out some heat.
It seems that the LMD's go through an erratic pulsing / stepper drive period before the thermal shutdown kicks in. (I presume it shut's off but not got that far myself)
Solution for me was to fit a 120mm fan to the top of the enclosure. Some form of active cooling seems to be required when at the top limit's of the ratings.
On a sidenote let's see what you have been upto and update your thread.