Battery powered Thermostat with "on/off" only function WiFi or zWave

Hi all.

I am searching for a battery-powered thermostat for cooling which can start my cooling system. I have a potential free on/off two wires. Currently, I have an old analog one which switches on when temp is below the one that is set. I want to replace it with one with a display for manual operation and in parallel through HASS.
Network can be WiFI or Z-Wave.
As I don’t have a power line on the wall outlet, It must be powered by batteries.

Any experience and proposals are welcome.

I suggest that you go for z-wave. Wi-fi will munch through batteries at an unacceptable rate.

I agree that zwave is better.
But can’t find appropriate device

Have you thought about 2 devices (a temp sensor and a relay) and an automation?

Yes but not usable in my case as I need the possibility for manual adjustment as well.
So I need a device that can help with that…

3 things? temp sensor, relay, knob input with the appropriate automations?

And display

Alternately build something with an ESP-01 and some sort of latching relay that is only awake for a few seconds every couple of minutes and in deep sleep the rest of the time.