This team does not shine early in the game, but it is hard to run all over them. The fact that you can not slowly poke down turrets vs. Heimer will often make the game long. He is very good at defending objectives.

Tristana is weak initialy and mid game due to lack of burst AP based dmg. Her range (550 at lvl 1) will pass Varus (575) at lvl 4, Ashe (600) at lvl 7 and even Cait (650) at lvl 12. At lvl 18 she has 703 range. She has a problem with freezing lanes, since her kills does AoE dmg. An idear can be to swich lanes the first few lvls. Tristana clears cs very fast and her range shines late game. Explosive shot decrease heals as ignite, so the team can go more for other summoner spells. Her escapes are extremely nice. Here you have a Tristana game where she shines due to beeing a very good counter to the enemy team: http://www.youtube.com/watch?v=7jDSF0TzxVE

Heimer as APC does not have much burst, but can farm some cs relatively safely even solo vs. two. His poke can be very anoying. While not feed he is squishy and quite easy to dive though. The risk is that he might land his stun/blind - especialy if you hug him. He sucks at roaming, but roaming agains him is risky because of his fast push. He does not burst like other apcs but has very high sustained damage.
His strength is that his two turrets apply his AP (100%) as magic dmg once every 1.3 sec and they have fine base dmg too. This is even doubled when turrets are freshly placed and they decrease both MR and armor and the damage has 40% splash AoE. Leaving turrets up when diving is almost not an option and taking time to kill up to 4 turrets or one Heimerdinger (GA?) will maybe delay you long enough to lose the fight.
As support he will passively heal as much as 20-25% of Sona's heal throughout the game and this affects everyone near him and does not cost mana. He has a blind that can also stun if you land it spot on, and his turrets will feed him more that other supports due to saving wards. Besides this he is still relevant when not farmed. Later in the game he can be a weak extra APC that is strong at dealing damage especialy defensively.
Heimer can win tornament games with his push (here as jungeler!!!): http://www.youtube.com/watch?v=r916C8O2HX or mid http://www.youtube.com/watch?v=l-J-dWba-6E or http://www.youtube.com/watch?v=QGnxZhDAzUQ.

TF is the APC assasine tp'ing to your ADC if possible. Very nice 525 range 2 sec stun and 1450 range poke skillshot that will often get dodged, but is great for clearing creaps and pushing. He can be build as ADC, but as APC you will often be able to 1 combo most opponents and with your ult and stun this is very powerfull. Mid game TF falls a bit off, but then his team might shine.

Cho can also lane, but I preffere him as jungler since he has some nice early CC, though it's all skillshots (one slowing movement 60% for 3 sec at lvl 2!). Besides this he brings 3 AoE abilities, build in sustaine and 2 smites to the jungle, so he will clear it very fast. End game he is the main tank and the first person to get low near him dies to Cho's powerfull true dmg ult.

Shen is more (TF) global presence and split pushing. He offers very nice protection for the team and can be there to taunt when Chos silence wears off. This provides great protection for the damage dealers.

Trist is basicaly not doing anything for the team other than staying safe and dealing damage. She might proc a slow with TF now and then, but it's not the point of the item in team fights.

Heimer is the support and he will heal everyone near him for 35 every 5 sec with his passive and Banner of command. This can combine with a Locket to 45 per 5 sec wich is very nice. A 0 ap Sona with maxed CDR heals the lowest allie (and her self) for 120 every 4ish sec so the sustain from Heimer is significant though not many realize it. It's roughly like 1/3 the regen from a baron buff.
Banner of command makes near by allied creaps hit a little harder including heimers turrets! 15% increased damage on both the base and the extra damage from AP is very nice.
Heimer also have nice vision with his turrets, his E (about 1000 range) and Twin Shadows. Wards helps too :)
It is nice to note that Heimer turrets will delay a diving teams damage because they have to clear them or suffer from there op damage and significant armor and MR debuff. AoE champs like Swain or Karthus will clear them with ease late game, but at least take a few hits and suffer some debuffs and they are quite easy to burst. TF's stun and Cho's knockup makes heimers E a much larger thread since you can expect to land the stun part much more often.

TF is the worst glasscanon of the team. Trist has build in escapes and stuff making her hard to kill, so she is a lot safer than TF, but TF provides a nice long lasting stun and a big burst. Besides this he has a 1450 range skillshot poke that might land in a confused team fight and he can ult in to finish off or even burst down single targets. His ult can also help Heimer with vision. When the oponent team is full health TF is probably the one on the team that should play safest cleaning up opponents that over extent. Hes stun will enable Heimer to land his normaly easily dodged skillshot stun.

Cho is the main tank. He is primarely preventing the opponent from taking down the teams damage dealers. He is very tanky even late game and has a silence that will delay the enemies burst and often allow Shen to join a fight that started bad for your team. He will be in the middle of everything and has multible auras.
He heals and buffs people with Runic Bulwark, he slows down autoattack damage with his Frozen Heart (1000 range) and he will debuff the enemy 20 MR with Abyssal Scepter. Besides this Shen's Sunfire Cape synegizing nicely with the last item.
His rupture often lands in team fights resulting in a knockup and a 3 sec 60% slow or at least zone people from running around freely. His ult 700ish true damage can pick off someone and change a fight. Cho's sustain comes from healing more than 150 per 5 sec when near to heimer so getting poked is not a big issue.

Shen is the teams primary split pusher. TF can sometimes do this job too, but shen is much safer due to his tankyness and dash. I already talked about his Sunfire Cape, but besides that he provides the team with healing in the fights via his debuff and Zeke's. Besides that he also debuff movement speed and armor when he attacks a target. To keep his team safe he has his ult shield and dash taunt. All this he combines with beeing naturaly tanky and having a nice shield for himself too.

The team fight items that I have not had room for in the build is first the mana regen aura item wich is not super valuable. A very nice item that I have not found room for is the 3 sec 40% movement speed buff from Shurelya's Reverie. Since the team does not have a Jenna, Sona or Nami helping on movement this is an issue. Besides this Mikael's Crusible would be very nice for helping out a single team mate, and that can be game changeing, but I have not found room for that either in the build. Cho does buy and sell a Locket of the Iron Solari providing everyone near with a nice shield mid game.