The Weekend's TV: Temple Grandin, Sun, Sky Atlantic <br/> Louis Theroux: America&rsquo;s Most Hated Family in Crisis, Sun, BBC2 <br/> Spiral, Sat, BBC4

As a "neurotypical" – as the autistic community sometimes characterises people not on the autistic spectrum – I'm reasonably adept at inferring other people's inner feelings from their outward expressions, but I'm pretty much disabled when it comes to imagining how autistic people see the world. There I need some kind of prosthesis to help me. Fortunately, there's a thriving industry in supplying them. There have been radio plays (Spoonface Steinberg), novels (The Curious Incident of the Dog in the Night-Time) and films, the latest of which is Temple Grandin, HBO's biopic about a high-functioning autistic woman who used her unique view of the world to build a career in animal husbandry. It's an odd kind of heart-warmer, which has the creation of a kinder, gentler slaughterhouse as its climactic triumph, but somehow Temple Grandin makes it work, in part because Grandin's particular mindset is so congenial for film. "I think in pictures and I connect 'em," she yells in the opening sequence, which could easily be a director's credo, too.

Mick Jackson began his film with a crash course in Temple's way of seeing the world, with a phrase or a thought instantly summoning a vivid image. "We get up with the rooster around here," her aunt explains, as the teenage Temple arrives to spend a summer on her cattle ranch, and you get a sudden cut to her and her husband perched on the eaves in their nightclothes alongside the cockerel. When Temple sees a ranch hand, a skitter of cowboy images riffle through her head, from cartoons and Westerns and old prints, and her mind also restlessly diagrams the world, overlying gates and levers with a kind of blueprint of their mechanisms. Temple, we learn, is a natural inventor, applying her talent to constructing herself a smaller version of the cattle press she sees being used to calm the steers. This, she explains, allows her to feel the comfort of a hug without the stressful element of human touch.

Claire Danes has already hauled in a stack of awards for her performance as Grandin, all awkward abruptness and panic attacks. It is, of course, the kind of role that is notoriously awardable, a perfect blend of affliction and touching human achievement. But there is real nuance here too, in the way that Danes shows you Grandin's increasing ability to manage her own panic and uncertainty. Encouraged by a passionate teacher at her high school, Grandin goes to college – where she does experiments into her own "hugging device" – and then on to study animal husbandry, where she begins to exploit the fact that she can empathise more successfully with cattle (as skittish and sensitive to noise as she is) than with humans. Although her suggestion that she write a thesis on mooing ("There must be a reason they're saying something") is initially mocked, she finds enough supporters to complete it, and to prove that going with the grain of cows' instincts might actually work. Grandin's Texan champions – who include the editor of the Arizona Farmer-Ranchman – are sometimes rough in their affection, but then she isn't easily offended by breaches of etiquette. "Use it, Temple," says the editor, planting a bottle of deodorant in front of her. "You stink." "Thanks," she replies, as casually as if he's just brought her a cup of coffee. The film ends with her addressing a conference on autism, exemplifying the pokerwork motto of empowerment the script returned to more than once, "Different but not less". And, yes, I got a bit teary.

In Louis Theroux: America's Most Hated Family in Crisis, Louis returned to spend more time with the members of the Westboro Baptist Church, whose version of Christian faith is big on homophobia, anti-Semitism and "God Hates Fags" signs. They deliver their breathtakingly odious beliefs with beatific smiles of certainty and curious kind of courtesy. "You're one of the chief workers of iniquity in the whole history of man," one believer equably told Louis. "You're up there with like Pontius Pilate and Pharaoh." This was down to the fact that it was in Louis's power to endorse the church, instead of which he keeps picking away at their belief system. So why did they have him back again? A church member explained: "Every time you do a documentary about the Westboro Baptist Church you're going to show those signs, aren't you, Louis? Thank God for the BBC."

The "in Crisis" bit of the title turned out to be a bit wishful. Yes, a couple of members had managed to escape the lunacy and appear to have survived intact. But their departure had only stiffened the resolve of the faithful who – however close they'd been to the heretics – stuck to the party line that God knew exactly what he was doing and would take his revenge for eternity. The group also now have a weird line in bilious pop mash-ups, adding lyrics of venomous religious piety to chart-topping hits. One hopes that the younger members might still be saved but for the elders who continue to feed them poison the suggestion painted on an opposition poster seemed most appropriate: "Drink the Kool-Aid already".

It's got subtitles. It's on Saturday nights. It has a female detective, comes in double episodes and mixes murder with civic politics. But that's where the similarities between Spiral and The Killing end in my view. If you happen to be a connoisseur of the art of dummy corpses this included a nasty masterpiece, but there's no substitute for Lund.

t.sutcliffe@independent.co.uk