The Tampa Repertory Theatre had a shaky start a few months ago with an amateurish Alcestis, but the current Cold Storage is so professional it augurs well for this company’s future. Ronald Ribman’s play is intelligent and affecting, and C. David Frankel’s performance as an irritating cancer sufferer is as convincing as any portrayal I’ve seen in the last year. True, the usually dependable Jim Wicker doesn’t come across as a German-born Jew, but Lauren Allison is perfect in the small part of nurse Madurga, and Keith Arsenault’s set (in the Studio Theatre of the HCC Ybor Performing Arts building) is as attractive and appropriate as the Alcestis set was rudimentary and distracting.

So TRT is for real: with a production like this, it demands our respect. It seems that any doubts were entirely premature. Cold Storage, directed by Connie LaMarca-Frankel, is the story of two patients, Parmigian (Frankel) and Landau (Wicker), who meet on a hospital roof garden and attempt with difficulty to reach some kind of understanding. It’s not immediately forthcoming: Parmigian, a spiky, thorny personality, is near-suicidal after too many cobalt treatments, and Landau, a more refined gentleman who’s in the hospital for exploratory surgery, mostly wants civilized behavior and a degree of privacy.

Parmigian gets the colloquy moving by asking Landau to push his wheelchair off the rooftop, and when Landau demurs, Parmigian admits that he just ran out of health insurance; only the proceeds from his fruit and vegetable business remain to fund his survival. “That’s what I dream about at night when they give me the morphine,” he says. “Floating over the rainbow on a shrinking carpet of tangerines.” Landau, an investment advisor in fine art, says strangely, “I have no dreams that would interest anybody,” but passing references to childhood experiences in Europe suggest that he’s hiding a traumatic past under his veneer of calm.

As unsuited as the two men are for each other, they achieve a level of trust; and eventually Landau tells the story of his past. It turns out his life hasn’t been as vanilla as it seemed. And pushy Parmigian isn’t as heartless as he pretends.

Frankel as Parmigian (the name is supposed to be Armenian) is a revelation. I’ve encountered Frankel often in his roles as assistant director of USF’s School of Theatre and Dance, and as artistic director of TRT; but only now have I discovered his impressive talent as an actor. Frankel’s Parmigian is self-pitying and aggravating, the sort of guy who’s not satisfied till he’s enraged you, who believes in nothing and wants to sting you into admitting that you’re a nihilist, too. He’s also a philosopher — and when he speaks of the impossibility of holding on to any gratification, you can’t help but see that he’s been defeated so often, he can no longer afford to turn his mind toward life’s beauty.

Wicker as Landau is persuasive as he fends off Parmigian in Act One. He’s considered where Parmigian is impulsive, decent where Parmigian is scandalous, and an apparent believer in the world’s value where Parmigian has decided that earth is a botch and a tease.

It’s only in Act Two, when Landau tells the story of a childhood in the Holocaust, that Wicker’s impersonation disappoints. He doesn’t have the look or the speech patterns of an American Jew (born abroad or not), and his rawest confessions suffer from the contradiction: just when we should be most moved, we’re untouched.

Ribman’s dialogue is erudite and emotional and at moments very funny. “You know what Spengler said after he got done thinking about The Decline of the West?” asks Parmigian. “‘I got a headache.’ The same thing was said by Hegel.” “How unpleasant a forgery is when you expected life,” says Landau. And “The Swiss never save anything but themselves.”

With dialogue like this and mostly strong performances, Cold Storage has as much claim to an audience’s attention as any show offered by a more established local theater.