Running with untuned antenna is bad... no antenna is even worse, and depending on the tx power setting, the chip may blow/ heat up. Bad antenna tuning / no antenna produces very high SWR and all the HF energy is reflected back into the chip, which easily explains the heating up of it.
I bought two of them bastards, under arduino IDE wifi works fine. Albeit when flashed ESPEASY it just keeps disconnecting. I was hoping to use it instead of regular nodemcu due to ext antenna...oh well. have to solder u.fl socket to nodemcu instead...
I assume that something about the internal antenna tuning / power adjustment / 'squelch' is different between the flashed codes,... or even he used SDK for the chip.