My HTPC uses a 2nd generation i3, but it is a mobile i3 (i3-2365M). The specs are about the same as that 2100 that you mentioned, but because my chip is mobile, it does not have as much power available to it and thus runs at a lower clock speed. There are other minor differences, but nothing too important for your usage. For low heat and fanless applications you are pretty much limited to mobile processors.
My conclusion: avoid the 2nd generation i3. I want to upgrade my HTPC as soon as the 11th generation mobile i3s become a bit more commonplace in HTPC applications (i.e. cheaper and more selection). Just the simple act of playing Pandora can overwhelm my CPU. Let alone all the CPU usage that Chrome has if you have more than a couple tabs open. It can run Kodi alright for movies, but I can see the occasional video stutter especially when upscaling old shows and movies to higher resolutions.
With each generation, processors have significant improvements in either functionality, power, speed, features, and/or efficiency (getting more work done at the same clock speed). There usually is a negligible price difference between generations, so you really, really want the newer generations and to avoid the older generations.
I'm waiting for more like this that are just now coming out (note: this has no memory, hard drive, or operating system, so it is not a complete computer, and it is not fanless):
https://www.newegg.com/asrock-nuc-box-1115g4/p/N82E16856158075
If money isn't too critical, $80 more for the i5 upgrade makes it a box that can actually play many games, although at low settings: