So as the title says, I LOVE Kobolds. I love them being tiny, mostly inept dragons. But for some reason I can never play them for too long because it begins to feel wrong. I've been thinking about it and here's why I think I end up dropping them. 

1) They are cold blooded. I love cold climates and Faerun has long winters according to their calendar, but the idea of playing a cold-blooded creature in a cold land is odd to me because they would be slower and unable to actually "survive" if my adventures bring him to Icewind Dale or Luskan.

2) It's hard to imagine them as heroes. Dragonborn are towering, able to kill with their breath alone, bulking. Something that feels like a hero or villain. But the kobold are small and lithe, it feels like it would be hard for something to "respect" a kobold no matter how high level they get. (That said, my kobold DID kill Acererak in ToA which was cool). In lore it feels like very few kobolds ever commanded respect no matter their abilities or skills, so would my kobold hero in Waterdeep ever actually be a hero?

3) When it comes to role-playing, kobold seem to be hard to get in the mind of due to their cold-blooded nature and their innate selfishness. If I wanted to do a kobold hero, it feels weird to break away from what kobold are already set as in the D&D-verse. (According to Volo's Guide, the most in-depth look at kobolds I've seen so far) They are selfish, spiteful, and bound to their clan or tribe. So, playing a kobold that breaks away from their clan to be a selfless hero seems too odd to me. Besides Deekin Scalesinger from the Dripping Fang clan in Neverwinter some 100 years ago I don't know if there's been another kobold hero.

I'll take any advice that can help me get into the mentality to stick with my lovely tiny dragon! Or maybe share tales of your own kobold? How did it work out, and how did you handle the problems I ran into?

My advice is to play the Kobolds from Mordenkainen Presents: Monsters of the Multiverse, which are not stated to be cold-blooded. The new Kobolds also do not have the cowardly or selfish traits associated with them from the Forgotten Realms, and the the multiverse Kobold's Draconic Cry inspires fear. Very respectable indeed.

this is a very subjective thing of course, just ignore this if it don't work for you, but here's my POV.

It's all about the number 2 in your list there. This is a joke race, it was made into a PC race for the lols of that 180 surreal POV juxtaposition, of what was originally created to be, just evil fodder for wanna be low level heroes to slaughter with impunity.
That is why there are Kobolds in the monster manual. We needed a little more variety than goblins and big rats for the noobs to lvl up on. And low level fodder, is low level fodder.
Also number 3 is right here too as you do spot. They were created to fill a function in a game system, whose function is to be opposed to the hero players of the game system.
Mostly suitable for a murder hobo crew, not heroes so much.

Making them a player hero race, is a joke.
Unless you wanted to be murder hobos of course, they do play well to that.

So there is my POV.
If you enjoy the joke, just run with it. If you don't, then see it for what it is and find something that holds the interest better.

On that tip, you could be short for a dragon born. And with the new system on the way, you can just say one of your parents was a gnome or whatever, and that's why you're clearly looking like a dragon born, just way shorter than most.

I'd also say on your number one on the list, Temporary Suspension of Disbelief is your problem there.
We're in a world of flying giant dragons that defy physics and and talking swords. Away put your knowledge of biology, it'll only interfere in your having a good time here.

"Making them a player hero race is a joke".

I'd say the joke is on the bandit who laughs at the "scrawny dragon-goblin" and then gets shanked, beaten to a pulp, pin-cushioned, or fried. They're in the same general size range as halflings and gnomes and have about the same body type as a dragonborn, so what characteristics exactly disqualify them that don't disqualify one of the current PHB races?

I've honestly thought of doing a character most likely an npc with the whole 3 kobold in a trenchcoat gimmick/joke. I'd probably have it played as an unintentionally hero. Things just happen to always go in their favor via random coincidence and the town all know but play along, until one day the real danger comes and that's when the party shows up to help with 3kb going along, and most likely getting/taking credit by the town when the bbeg is defeated

If you love them, then play them. It's not harder than any other race. They are really great in any group.