It looks like CPU does not enter any kind of low power mode while charging now leading to shutting down the battery charging due to overheating (well, the CPU sensor is overheating, not the battery itself, though it does get warmer due to being physically close). This needs to be investigated.
It appears to be related to some user-space application. In my case disabling Google Play immediately stopped the extensive CPU usage (even though it was not really being used as far as top was concerned).
Still needs more investigation.