stuck on 39937

Try adding the following line to conf/heat.properties:
heat.enableHallmarkProtection=false
This is not a normally recommended setting, but it might help things out until HEAT gets more hallmarked nodes.
Again to stress: is not normally suggested, only at this early stage.
EDIT: The reasoning behind this suggestion is that there are comparatively few hallmarked nodes on the network. If any hallmarks get on a fork (especially the ones with bigger accounts), they have a very high influence on remaining nodes because those nodes "trust" the hallmarks more than everyone else. This makes it hard to follow other chains if they are held by non-hallmarked nodes, even if the forging rules declare it a stronger chain.
As far as I know, the single biggest reason for hallmark protection is to prevent Sybil attacks. This is a desirable feature of a P2P network which is why it's not typically recommended to disable. We as a community should strive to have more good hallmarked nodes on the network. But for now maybe disabling it helps to stabilize??? (not really sure)