Depends on what you’re trying to do. The simplest being you can buy an portable A/C, Heater and temperature sensor and hook it up to a SmartPlug which can all then be managed by a compatible Thermostat SmartApp to control the temperature in the room.
Or are you looking for a A/C / Heater which can natively be integrated into SmartThings, your options here will be a lot fewer.
Most A/C units use IR for control. Get yourself a Logitech harmony hub (currently £49.99 on Amazon) which integrates with Smartthings and then use this to trigger heating/cooling activities. That’s what I do with my LG ArtCool split system.
As mentioned by @Shinedown78 most AC systems use IR remotes for control. They can be therefore controlled by Logitech Harmony which has integration with Smartthings although I am a little dubious about how much AC specific control this would expose.
All the various ‘smart’ systems for controlling AC systems that I am aware including Tado Smart AC, Sensibo, AirPatrol and AmbiClimate also use IR to control the AC system. Some of these can be used with Smartthings either via apps or IFTTT.
However another approach is specific for the Daikin range of AC systems. Many of these support a Daikin module for controlling their AC unit via their app over WiFi. There is a matching user contributed Smartthings app.
Since this is a direct link it would in theory be more reliable and allow some bi-directional reporting like its own temperature setting.
Disappointingly Daikin have not progressed their WiFi controller further to have official integration with any smart home platforms other than IFTTT. I would have liked to see them add HomeKit and official Smartthings support amongst others.
@Neil_McRae Neil apologies I was away for a few months. Sensibo has a USB powered IR sender that you connect to your wifi. The app covers just about all aircon units. I have a cheap Spanish brand and it was literally plug, select aircon, play. It is around £99 but it give you things like aircon timers, operating louvres, filter alerts. Actually it gives me more than the remote I got with the aircon does.
Why not just buy a Samsung heat pump? Works directly with smartthings. We have both a heat pump with sensibo, and another Samsung heat pump. Next time I change one in either of the houses I will go for Samsung again…
I could not find any mention of support for Smartthings on the UK Samsung heat pump and air-con website. I did find mention of a WiFi module and would hope that via it it could be linked to Smartthings - but as I say it does not mention this.
It should also be noted this only showed up on their business website as well making it even harder for me as a consumer to find.
I think the reason for the heat pumps being on the business side is due to regulatory laws that state that you cannot install heat pumps and ac systems yourself, at least here in Norway. Has to be a certified installer.
However, here is a link to ours, in Norwegian, but there are pictures.