Ultimately you're maintaining an average temp anyway.

When you say unstable, in what regard ? under what circumstances ? Most temp sensors are very slow responding anyway, so naturally damp out things.

The ecu temp sensor would need to be within the engine so to speak, engine block, head etc are all good spots, where water is always circulating. Beyond the T-stat, this may not always be the case, although with the engine warm, there would almost always be water moving even on the rad side. Not so much during initial warm up