Unfortunately for cool space battles, no this still doesn't work for the reasons outlined.
First off you have to remember that when a ship turns it's engine on it's going to be visible effectively to the entire solar system unless there is a planet or something in the way. We already have the capability that we would notice a ship moving in the asteroid belt from Earth and in the Expanse it's going to be even higher. So everyone already will have known when you turned your engines on and can run the calculations to see where you are while you are coasting, so even within the confines of the fiction that shouldn't work.
But let's ignore that and say that for some reason no one was looking when you turned your engines on. Assuming your ship is somehow running with all systems off it's going to be roughly 300 C hotter then the vacuum around it, even with a heatsink like you mention (and a heatsink that can store that heat for months is also unrealistic) you're going to be sticking out like a sore thumb to any infa-red. You're just too hot.
First off you have to remember that when a ship turns it's engine on it's going to be visible effectively to the entire solar system unless there is a planet or something in the way. We already have the capability that we would notice a ship moving in the asteroid belt from Earth and in the Expanse it's going to be even higher. So everyone already will have known when you turned your engines on and can run the calculations to see where you are while you are coasting, so even within the confines of the fiction that shouldn't work.
But let's ignore that and say that for some reason no one was looking when you turned your engines on. Assuming your ship is somehow running with all systems off it's going to be roughly 300 C hotter then the vacuum around it, even with a heatsink like you mention (and a heatsink that can store that heat for months is also unrealistic) you're going to be sticking out like a sore thumb to any infa-red. You're just too hot.