A 74HC123 / 74HCT123 datasheet here draws 8 uA max at Vcc=5.5V at 25C. That's for the IC itself - current in the timing resistor will add to that.
A lower current option is to build an oscillator from a single Schmitt trigger gate. Supply current is typically 0.02 uA and timing components add perhaps ~= 0.5
uA - less if care is taken.
At 5V a CD40106 (hex Schmiit inverter draws 0.02 uA typical, 1 uA max at 25C.
See datasheet for other conditions.
Using a 10M feedback resistor and around 2nF cap an oscillator using one gate will draw around an additional 0.5 uA or less for the capacitor driving. Ground the other gate inputs and leave the outputs open.
Icap is i = V/R = (Vhigh - Vschmitt low)/10M when the capacitor starts to charge, falling to ((Vhigh - Vschmitt high)/10M just before the gate switches. As the low and high thresholds are in the order of Vcc/3 and 2.Vcc/3 the charge current with a 10M resistor should vary from about 2/3 x Vcc/10M to 1/3 x Vcc / 10M as the capacitor charges or discharges.
A larger resistor than 10M may be used if due attention is paid to leakage paths and environmental cleanliness.
The gate internal currents may change as Vin = Vcap transitions exponentially between low and high states and this is not well covered by the data sheet. Experimentation (or simulation) will be required to confirm current drain, but it is liable to be low.
simulate this circuit – Schematic created using CircuitLab
how stable is this with changing temperature when using it ouside?
At exactly 25 degrees C it's perfectly temperature stable.
If you have more details of what you wish to achieve you should place them in your question. Otherwise we go around and around and ... in circles and waste your time and ours.
What stability spec do you want?
What is your expected temperature range?
Next will you ask "and what about voltage variation", and humidity, and .... ? Resistor and capacitor variation with temperature may matter.
Device threshold variation with temperature MAY be in the spec sheet - did you check?
We can try to help, but knowing what you want is essential.