I know some physics and have a coal oven in my Berlin apartment, so I feel I can chime in here. A chimney works (ignoring wind for simplicity) because the hot air is lighter than the cold air in the environment (room, outside air) and therefore rises. An upward draft is created. At least old-style ovens and chimneys are not hermetically sealed; the gaps don't leak exhaust but instead draw in air because of the under-pressure in the chimney.

The system works because air can flow in from below (this lacking is the sealed room problem) and because the air in the chimney is hotter than the environment. That the chimney works at times indicates that the room is not sealed (that would be constant) but that under certain conditions the draft is not sufficient (which can be intermittent).

Now the reason for lacking draft, absent wind, is that the exhaust stops being hotter than the environment. This is obviously more likely when the outside air is warm, which is what you experience. (This is less likely a problem with room heaters than with water heaters because rooms are typically heated only when the outside is cold while water heaters are running all year long.)

Apart from a warm outside, a cold chimney with high heat inertia (e.g. a brick chimney that needs a while to heat up) may contribute to lacking draft: The rising air cools, becomes heavier than the environmental air, and sometimes outright "falls back" down, all the way into the room. This can be a bit self-reinforcing: The hot air never reaches the upper parts of the chimney which therefore stays cold.

With a coal oven this can be overcome by burning something like bunched up newspapers with a large, hot flame which breaks through that "cold barrier". Once the chimney is hot the draft is usually sustained because, of course, the exhaust of a regular stove is in principle still hotter than the environmental air.

While that solution is not available to you, another one may: You should have a better draft also when the upper chimney is less cold. You may be able to heat the places the chimney goes through on the way to the roof so that the chimney is not cold. Other than that: Longer chimneys also improve draft. Extending your chimney upwards may bring an improvement as well.