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"Find And Replace": 60-year-old Jo meets up with the Third Doctor (and Benton) back in the 1970's. It's the sweetest thing in the history of anything ever.
In "Death In Blackpool", the Doctor and Lucie pick up a drunk guy dressed as Santa Claus. He turns out to be an average guy who lost his job, and Christmas turns out alright for him when he charms the hospital lobby personnel and gets a job offer as a porter. No heroics for him, no aliens, no big sweeping space story — just a nice Christmas with happy Christmas songs. He remains completely oblivious to the plot.
In "The Wormery", Iris Wildthyme makes a good show of stating she's not attracted to the Sixth Doctor (much as she fancies his other regenerations). As soon as it seems like he's falling for Bianca, though, she gives him an Anguished Declaration of Love that actually manages to be on the sweet side of Yandere. As much as they usually bicker and complain at each other, the audio shows many aspects of their Odd Friendship over the years, and how much they're willing to help each other out when push comes to shove.
"Thicker Than Water": Evelyn's big damn platonic "I love you" to the Doctor. And just before that, the Seventh Doctor visiting Evelyn in the hospital, unannounced and uncredited, just to tell her that his companion Hex is Tommy, Cassie's son.
The Wrong Doctors provides a simple and very sweet explanation why the Sixth Doctor, who over time (in Big Finish) had swapped his technicolour nightmare coat to one of calm blues, decided to change back. A Mel Bush from his own future is being unwritten from time, and in her last moments quietly admits ...she actually quite likes his patchwork rainbow coat.
Sixth Doctor: Then I shall wear it again, for you.
In the TV Mini-episode "The Night of the Doctor" the last words of the Eighth Doctor are to remember his companions from his Big Finish adventures. Which is heartwarming both in the direct sense (as even during the madness and carnage of the Time War he never forgot his old friends) and in a Meta sense as it officially brings them and the rest of BF's Doctor who stories into full Canon.
The entirety of Signs and Wonders; seriously, this troper had to fight the tears that came to his eyes. Spoilers abound:
Though sick and dying, Elder God To'Koth asks for the Doctor's help to return to its old realm so as to not damage Earth (and the reality it was in) with the energies its death would unleash. It takes even the Doctor a while to wrap his head around the idea of an altruistic elder god and of one permanently dying, and it nearly destroys him and his TARDIS to honor the request. The reward? An end to the hostilities between himself and the other Elder Gods, putting to bed the Seventh Doctor's crusade against them.
Fifteen years after Hex has properly returned to life, he and Sally Morgan have settled down and had a daughter, with another child coming on the way, and Hex is devoted to not missing a moment of their lives after missing the deaths of his mother and grandmother. What is their daughter named? Cassandra.
In Afterlife, part of "The Reason You Suck" Speech Ace gives the Doctor is that he never showed her how to pilot the TARDIS, yet had taught two much more recent recruits to do so, as it "wasn't part of the plan". Here, the Doctor invites Ace to pilot them to their next adventure, without a hint of manipulation.
In 'The Fearmonger', Ace's worst fear is that the Doctor would go evil. You can practically hear the smile in his voice as he says that he should be flattered.
It's implied that the Doctor's worst fear is Ace getting shot. Which just happened. And that's the reason that he isn't afraid of the Fearmonger.
Doctor: Go away. I have more important people to worry about.