Graphs showing relationship between CO2 and temperature anomalies (HADCRU5) using annual data from 1959 thru 2021.

Basic OLS output:

No evidence of positive autocorrelation.  R-sq is very high.  All coefficients are significant.

Further ACF graph shows no evidence of autocorrelation in the residuals:

What about normality of the residuals.  Cannot reject normality:

Here is a graph showing fitted versus actual:

I am not particularly recommending this model.  It has lots of problems.  My only point here is to show that the results of the regression depend on the start date.  Including a lot of very early CO2 data convolutes things because of various regime changes.  Using later data better captures what's going on in more recent times when CO2 emissions have become a much bigger problem for lots of different reasons.