Observations after a couple of days:
I have run both - the now refurbished [and unexpectedly returned] Inspiron 5510 from my 1st post, and my new Inspiron 5410 14" (the one I thought I needed because I was supposed to get a refund for the returned 5510.) Both are running fine. And I like both.
I never owned one so after Wynona suggested it, I purchased this
Kootek cooling pad from Amazon in anticipation of my new i5 14" needing a little help. The cooling pad does make a difference, but my not-very-big abuse right now is streaming radio or the occasional video. The i5 5410 runs very well, even with only 8GB RAM. Overall about 35-50C with several websites open, Thunderbird, and streaming SiriusXM radio, or a Prime movie.
Comparing those same conditions, the refurb'd i7 is also keeping its cool just fine. Before, my i7 5510 would spike often at 96C. Now after a few days the i7 runs at 35-45C, and rarely gets to 55C. I'm liking it a lot more now!
Could be that i5 5410 works a bit harder to keep up? (It isn't really working very hard, but I ordered replacement 16GB RAM.)
Still no email or other notice from Dell that I'm actually getting the 5510 back; it's all configured, updated, running great. Still waiting to see if daughter gets the promised refund; might take a few extra days with the holidays approaching.