2. I swapped the power supply with a simple one built around 3.3V regular - no luck. Tried powering it from USB-TTL 3.3V (connected to a hub). The chip started getting warm then USB channel went down. So I don't think the power supply was at fault.
3. I had originally only connected power and serial, so if connections were faulty then I would not have seen any response to AT commands. I have logged humidity data overnight to emoncms without any issues. I bought 2 chips from the eBay seller and both have same temperature problem.
I think there might a problem with the batch of modules which I got.