An analysis by month shows a similar pattern for the entire record and the best fits for each month displays a similar pattern. The following table gives the period, amplitude and phase for the fundamental frequency of the best fit. April appears to have the longest period and October has the largest amplitude. These months are mid spring and mid autumn although this might not necessarily be significant. One has to ask if these changes are due to oscillations or if they are just fluctuations in the temperatures which appear to be oscillations. To assert that these "fluctuations" are oscillations at this point would, in my opinion, be "deeming" them to be so. The cause of these fluctuations needs to be determined if it is shown that they are not just random fluctuations.
The coefficients for the quadratic portion of the fit are given below. The columns are the months, the mean values, the rates of change and half** the "accelerations" for each month. Note that on average the rates of change indicate both increasing and decreasing trends depending on the month.
*edit: The available data is from Jan, 1880 through Nov, 2009.
** 2nd edit: The numbers are just the quadratic coefficients and represent values at the beginning of the curves. One would have to set yr to 129 to estimate the 2009 values. The fit used 0 for the Dec, 2009 value which would add a slight error for the Dec curve.