What about the temperature ?

I dont follow, what is tempe?

and why we are speaking about something external? 

For those of us who want a fairly accurate record of temperature during s ride it's the work-around to the problem that a Garmin Edge will always be vulnerable to heating by the sun and give an unrealistically high temperature. The Tempe temperature sensor can be placed in a better shaded location on the bike. On a cloudy day the Edge 1040's temperature is close to the coorect value.

I think my 1040 reads temperature ludicrously high (maybe even more ludicrously higher than my 1030). It does not bother me too much as I didn't buy it for reading temperature. However, I think the solar charging uses it as well and shuts off when the sensor reaches a threshold maybe sooner than necessary as the sensor is reading too high (again, for me it's not a major issue as solar is more of a "top-up when available" rather than pirmany power source).

It seems New edge explore 2 has native support for tempe. Will it be supported by edge 1040?

Temperature in Edge 1040 for me works dramaticaly incorrect, this reading is useless.
In my today commute ride I was riding with Edge 1030 (not Plus) and E1040 Solar. Morning it was quite sunny, on E1030 temperature about 21-22'C, on E1040 25-26'C. In the evening it was raining and much cooler. E1030 showed 10'C but E1040 only 8'C. So when is hot - E1040 shows temperature much too high, but when is cool shows too low.

Temperature in E1030 isn't perfect, but is stable, it shows about 2'C too low, so when is freezing it shows -2'C. But temperature in E1040 is completely unreliable.

Come on Garmin - it can not be like that!
This is your premium model, we paid for this a lot of money and we have right to respect quite stable temperature readings, it is not quantum mechanics to do something like that. You could implement temeprature readings quite stable in older models - so you can in 1040, your customers expecting this. I remember that in E1030 it was fixed by firmware update (update 3.77) so you can also fix this in E1040. Temperature is really important parameter for many cyclist, you can see this how many replies are here.

Tempe is an external temperature sensor from Garmin. Connected via ant+ it displays temperatura data on fenix watches but no natively on the Edge 1040. But it seems so on the Edge explorer 2 a lower end model

Something that Garmin could easily do is to utilise the brightness according to the ambient light sensor to apply a negative correction to the measured temperature to offset the heating by the sun. ie no correction under cloudy conditions and progressively reduce the measured internal temperature depending on the light intensity. There would need to be some smoothing built into the correction because the temperature doesn't quickly fluctuate when moving between sun and shade but that's easily done.

Or simply add native tempe support to the 1040 as the lower model explore 2..if you want a very reliable temperature daya

I don’t know of any temperature probe (even costing $500+ on its own) that when it’s exposed to sun will read correct. Ideas of somehow applying a correction factor based on the sunlight sensors are just wishful thinking. On a cloudy day / in shade, you could expect it to be within +- 1-2°C.  As it happened yesterday I was riding in around 30-31°C in partly cloudy and the unit was giving me exactly that.