Immediately below is an illustration of my first/prototype attempt to visualize this, which is further explained after that...
What you're looking at is a year-by-year animation of TMAX (daily max temp) data from the USW00094728.dly file (station at Central Park in New York City) openly available at ftp://ftp.ncdc.noaa.gov/pub/data/ghcn/daily (see the readme.txt file in that directory for file format info, etc).
The left-hand-side of each frame is Jan1 TMAX and the right-hand-side is Dec31, whereby each frame represents a full year. And the years are 1870 through 2009, each year displayed for 0.2seconds. Two blank frames signal when the animation repeats. The temp scale is $40^o\mbox{C}$ max, $-10^o\mbox{C}$ min.
Also, the daily TMAX data in the displayed animation has been smoothed, i.e., each day denotes a seven-day average including the three days before and after it. Without that smoothing, it's really, really jumpy/discontinuous.
Nevertheless, even with smoothing, there's no TMAX change discernible to the casual observer during the 140 years represented. Of course, with an expected $1$$2^o$ change on the $40^o$ plot, that might just be too hard to casually notice.
So several ideas occurred to me. (a) Maybe subtract out the daily means (averaged over the 140 years), and display a $\sim10^o$ plot, whose higher resolution would make the small delta's more easily observable. (b) The seven-day smoothing, separately over each year, may not be enough since the year-to-year data is still very jumpy. So maybe additionally smooth by averaging the same day over several before-and-after years. But then that may just be too much unjustifiable data massaging.
So, the overall question here is: what-to-display/how-to-display-it so that the ~150-year TMAX change is easily visible and easily explainable/understandable to the casual observer. Any average person-in-the-street should just be able to look at it and immediately see what's happening, without any gobbledygook/gibberish technical explanation necessary. Also, a side-question: it took a while to find that noaa ghcn data, which seems terrific. Any equally-good or better openly available datasets around?
EDIT
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Thanks for the comments, @JeopardyTempest and @CamiloRada.
JT's "nighttime low" suggestion (TMIN element from ghcn data) is easy to exhibit, just requiring different command-line arguments to exactly the same program (no packages, by the way, all straight C programming, which I mention after noticing "Programmer" in your profile). So I've illustrated that TMIN animation below (scale, etc, identical to TMAX animation above). However, as pretty much expected, still no easily-visualizable change over the 140 years.
We'll have to try "using anomalies", quoting CR, and hope for better results. And that's probably a reasonable hope, based on your youtube link, which is pretty much exactly what I think I'd be generating, except with Jan,...,Dec along the x-axis rather than the "circle graph" displayed there. (By the way, while it's easy to interpret that circle graph, I think maybe the average person-in-the-street might more easily recognize the left-to-right months-along-the-x-axis display, which is probably what most people are already more familiar with.)
And I'll also take a closer look at that HadCRUT4.4 data used by the youtube's homepage http://www.climate-lab-book.ac.uk/2016/spiralling-global-temperatures/ Google hadn't coughed up that data during the searches I'd tried, and I imagine there's lots more good&interesting stuff I've overlooked.
Meanwhile, immediatly below is the TMIN graph suggested by JT. The "anomaly graphs" will be easy to animate after I code the across-the-years data "select"ion (i.e., analogous to a relational table) from the ghcn data. That'll take a bit of doing (in my available spare time), and I'll try to post some better temperature-increase visualizations when it's done. JT's more elaborate display suggestions will take a bit more elaborate thinking and doing (moreso on the display side than on the computational side), which I'll try to plan/design as I'm coding the more straightforward "anomaly" stuff. Thanks, again, JT and CR.