So the Washington Post tracked him down at his studio in Carthage, Missouri, to ask the burning questions.
What is going on in this painting? Where even is this?
I put it in a private-club type thing. Not a restaurant, not a bar, but a private club. It shows all of the Republican presidents, some of the more major ones in the foreground, but they're all in there.
They're kind of story-telling. Lincoln and Trump in particular are relating, and everybody else is reacting.
What are Lincoln and Trump saying to each other?
I have no idea. That's the funny thing: We don't know how they would get along. Just because they're all Republican doesn't mean they actually like each other.
How did it end up in the White House?
I once painted [California Republican congressman] Darrell Issa's portrait. We got to go to Washington, and Darrell gave us a tour. He had both of my original paintings in his office, of the presidents playing poker. We stayed in touch. Darrell's a real friendly guy. He contacted my wife, Dina, one day and said: "Gee, I saw you've got a new one. I'm going to show it to President Trump."
[An Issa spokesman confirmed this account to the Post: "Rep. Issa and Andy Thomas are indeed friends, and the Congressman has some of Andy's fine work in his office. President Trump appreciates the art that Andy does and the Congressman did deliver the portrait to the White House."]
A couple weeks ago, we got a call. Somebody at the White House said, "Trump wants to speak with you." Sure enough, he did.
We had a real nice conversation. Trump said something like "I'm in the Oval Office with Darrell Issa, who you know, and Vice-President [Mike] Pence. We're looking at your painting. I've never seen this! Vice-President Pence tells me they're very well known."
I remember he said he's seen a lot of paintings of himself and he doesn't usually like them. He liked that one. He kept talking about my talent and this and that. He asked a little about politics. It lasted three or maybe four minutes. I hung up and said, "I'm too good to go out and finish mowing the lawn." (Laughs.)
So Trump doesn't have the original painting?
It's a high-quality laser print. The original is still in my studio.
Trump does look pretty good in your painting. He actually looks more athletic than he does in real life.
I wanted to make everybody look as good-looking as they can, and try to shed the pounds where I need to. Or smooth some lines. I did it with every figure.
His smile is very charming. I don't think I've ever seen Trump smile like that.
It's a good-feeling painting. I just assume people are nice. I try to make people as good-looking and happy as I could.
The first painting I did in 2008, originally I had Richard Nixon looking paranoid and covering his cards. I thought about that and thought: "That is not right. The poor man suffered from clinical paranoia, I shouldn't be making fun of it." I intentionally look for happy pictures.
With Trump, I looked through just a tonne of photographs. Some of the presidents smile naturally every time, and some don't.
This is the second face I painted on Trump. The original one, I had a very sweet picture of him smiling with Melania and maybe his grandkids. It was very becoming of him, but it didn't look as much like Trump as it should.
Is Trump drinking a Diet Coke?
Yes. I researched it.
What's Reagan got there?
I put what looks like kind of a fruity drink. Reagan's father was an alcoholic. I don't want to show whiskey in front of him.
And George W. Bush?
Iced tea. And Nixon enjoyed a good glass of wine.
And Lincoln?
Water. This is mostly researched off the internet. I really don't know.
I've heard there's some significance to the woman in the background.
That would be the first woman Republican president. I did the same thing in the Democratic painting.
Is your work styled after other artists?
I always liked the American illustrators. I do primarily Western paintings - cowboys and Indians. Frederic Remington and Charles Russell are two of my favourites. And Howard Pyle. And some Norman Rockwells.
But I've been doing artwork all my life - since 1990, full time. I'm 61 years old now. It becomes your own style.
Now that your painting is all over the Internet - and because everything with Trump is so polarised - some people are making fun of it.
[Laughs.] I'm used to it. It's kind of discouraging that sometimes people are so venomous, but that's the way it is. I just paint! It's kind of a nice life.