The timer should send every minute, not every 13:59 hours.

there is no way to set it every minute:

If you like to send the real temperature you have to replace 00 D7 by the temperature-value HEX(highbyte(temperatur10)) HEX(lowbyte(temperature10).
But for first test i think you can use a fixed value, maybe send more often (15 sec) and see if the thermostat shows this value as outdoor temperature.

BTW: you can log the telegrams and click download, safe it to file an drag/drop the file here. This is much better readable that screenshots with only a few lines.

Ok, than it is much more complicated to emulate this sensor.
I'll try to make a emulation with register device 0x50 including version repyl and send temperature periodical. Will take a bit.
My system in ems (not ems+) and has a physical sensor connected to boiler, so can't test the virtual.
If the test is ready i will inform you for testing.

Please try this build: https://github.com/MichaelDvP/EMS-ESP32/releases/tag/test

You should find in settings application a checkbox for Emulate outdoorsensor:

If enabled there should be Wireless sensorbase detected in devices with outdoortemp 0°C

Edit it to the actual outdoortemp, or use connect/outdoortemp as api/mqtt/telent command.
Then try if your thermostat detect the temperature right and allows to configure to outdoor based control.

Make a log of the communication to see if thermostat tries to get more values from this device.

You have to disable the system send command, this is now a bus-collision. Please make the log a bit longer (~5 minutes).

I rewrited it to use "outdoortemp/connect" instead of system/send but I've got wrong temperature:

{
    "outdoortemp": 50
}

I sent temp: 50 00 D1 00 00 14 = 2*C // Ok, changed to decimal instead HEX...

You have to send connect/outdoortemp with a single value e.g. 9.7, but this is not needed to repeat frequently, you use this command only on change of external temp. For testing you can just use the web interface and click on the pencil.

But looking on #1584 with much communication to the sensorbase it's maybe much more needed to emulate the sensor. We have to try step by step.

It's working
{ "outdoortemp": 2 }

I can't see outdoor temperature at thermostat - should be visible at the screen

I think you have to configure it in the thermostat standarddisplay settings.

but the temp curve is ok

That's a step forward. Is it now possible to set the controlmode of the thermostat heatingcircuit to outdoor (weather compensated)?

but at Buderus I can see new flashing icon:

controlmode of the thermostat heatingcircuit set to outdoor (weather compensated)
but
I can't find at thermostat standarddisplay settings to view outdoor temperature

You have not send the system info, so i don't know what thermostat you have.
The RC300 manual says there is in general settings a menu standard display and you can choose, different temperatures (solar, outdoor, etc . to show in the upper right corner. Check the manual from your thermostat.

sorry it's rc310 and yes, I found it. It's already set to outside but temperature is still missing.

I have compared the logs and (so far) did not find any differences. The thermostat calculates the damped outdoortemp correct and is set to room+footpoint control. So he gets the outdoortemp correctly. Don't know why you can't show it on the main screen. Does other settings work?
I've changed the test build back to simple wireless base without extra T1RF.

Does other settings work?

actually, I can't set to controlmode of the thermostat heatingcircuit to outdoor.

It seems that the outdoor temperature is available, but the sensor itself is not recognized by the thermostat. Therefore, I cannot set the boiler to operate based on the outdoor sensor.

I can't set to controlmode of the thermostat heatingcircuit to outdoor.

Oh, sad. I'm out of ideas.
Can you log and restart the thermostat/heating, maybe we miss a query to the wireless base.

Have you ever tested with the F7 commands i've mentioned?
As maybe better variant: With outdoorsensor enabled send call system send "50 10 F7 00 D1 00 00 03"
(or try call system send "50 00 F7 00 D1 00 00 03")

Have you ever tested with the F7 commands i've mentioned?

yes, without success :/