There are a number of “heavy duty” appliance modules, most rated at 15 amps. See if those match your device specs.
Don’t use the 12 amp plug if that’s not rated high enough to carry the needed current for your devices, there is a real danger of fire.
Here are some alternatives:
The GE 12719 is rated for 15 amps, but check the specs on any model you’re considering, as they make several devices that look very similar but have different specs.
The DragonTech appliance module is rated for 15 A, uses zwave plus which gives it longer communication range then older zwave, and may be the least expensive at about $28, but note that it does not have a second pass through outlet which some of the others do.
There are more as well, these are just some examples.
If by chance your air-conditioner requires 20 A, there are solutions for that as well but only ones that require wiring into the circuit or replacing the in wall receptacle, nothing that just plugs in. 20 amp receptacles have the T shape socket.
There are also some micros which can get wired into a circuit and control up to 40 amps.
So you will have choices, but always make sure that the network device you’re using is rated for power at least as high as the device you’re going to connect to it.