If it is reasonable to assume linear trends you can use a simple linear model to estimate the slopes and a possible difference between the slopes (of the two decades).

Your response (let's call it "temp") is the vector of temperatures.

You would need to code your predictors as follows:

"decade" should be a factor with two levels, one for each decade,

"time" should be a time value (like days) relative to the start of the respective decade.

Given "temp", "decade" and "time" are vectors containing your data you can fit a model in R with

model = lm(temp ~ decade*time)

This model fits two straught lines describing the tempretatures over the two decades.

You can get the estimates (with standard errors and all that) of the coefficients with

summary(model)

The meaning of the coefficients is as follows, assuming the order of the levels in "decade" are "80", "00" (the first level refers to the 1980s):

"intercept": expected temp at the beginning of 1980s

"decade00": expected difference in temperatures between the decades at the beginning of the decades (2000s vs. 1980s)

"time": expected change of temperature in the 1980s decade over time ("slope" in the 1980s)

"decade00:time": expected difference in the slopes between the decades.

The last coefficient is called "interaction" (between time and decade) and tells you how much different the two trends should be expected to be.

This is a simple task.

Use Mann-Kendall test.

Dear Luca

Maybe you can use Statistical Process Control (SPC) tools. SPC tools are used to monitor one or more quality characteristics in the process. In above case, you want to monitor temperature and test whether the fluctuations in temperature are random or follow a pattern i.e. trend(up/down), shift (up/down) or even cyclic!!

I hope you find reading some literature on SPC, control chart and control chart pattern recognition useful.