For me your command doesn't run. I run:
t =
QuantityMagnitude[
WeatherData[
"California",
"MeanTemperature",
{{2013, 1, 1}, {2014, 1, 1}, "Day"}
]["Values"]];
This contains all temperature quantities.
A list of dates in your period is easily constructed by
DateRange[DateObject[{2013, 1, 1}], DateObject[{2014, 1, 1}]]
so the association array you're looking for can be obtained from
AssociationThread[
DateRange[DateObject[{2013, 1, 1}], DateObject[{2014, 1, 1}]] -> t
];
edit
In fact, a neater way to achieve this is:
t = WeatherData["California", "MeanTemperature", {{2013, 1, 1}, {2014, 1, 1}, "Day"}];
Association[Rule @@@ MapAt[DateObject, t["Path"], {All, 1}]]