I would start by re-shaping your data into a table where each row contains a "response" (the duration of hibernation), your predictors (ground temp, air temp) and any other info to include in the mode (year, turtle etc). Something like this:

Hibernation_duration    Turtle   Year   Air_temp   Ground_temp
                  40         A   2015         24            15
                  35         A   2016         27            16
                  41         A   2017         24            15
                  34         A   2018         27            16
                  43         A   2019         24            15
                  33         A   2020         27            16
                  45         B   2015         24            15
                  32         B   2016         27            16

etc...

It sounds like you have defined your response already. However, you may need to give some thought to how you want to define your predictors. e.g. you could use the mean temperature for that whole year, or you could use the mean temp over the two weeks prior to hibernation. You will have to use your expert knowledge to decide what is appropriate. If you include multiple predictors (i.e. ground temp and air temp) check that they're not too correlated - variation inflation factors are useful for this.

You can then use a generalized mixed model to test your hypothesis. As vkehayas notes in the comments, you will need to decide what distribution to specify for your response variable - gamma may be appropriate as it is bounded below by zero, but has no upper bound. You don't want to be able to model negative durations, although if they're high enough, a normal (Gaussian) distribution may also work.

If you're using R, you can specify a generalized mixed model like this:

library(lme4)
model <- glmer(Hibernation_duration ~ Air_temp + Ground_temp + (1|Turtle) + (1|Year), family=Gamma, data=data)

Here, Turtle and Year are included as random effects (Note, you would have to convert Year to a character/factor variable first). You could do some reading around these to understand them more, and how they're useful for your type of study.