Thermostat Card with rest_command

Hello everyone! I am using a (not yet supported but soon) Broadlink RM4 to control my Air Conditioner.
As my Air Conditioner is also not supported by Broadlink, I had to record every configuration using Broadlink’s app:

  • set 20C low
  • set 20C medium
  • set 20C high
  • set 21C low
    … and so on.

Gave me some work but it actually works quite well.
I can also control it using REST commands to bespoken.io through Alexa.

Now I wanted to integrate it with Home Assistant using a Thermostat card. The main idea would be to send a rest_command for the chosen temperature every time I change the value on the Thermostat card.
So, for instance, if I pick 21C in the Thermostat card, that would send the following command to Bespoken.io:

curl "https://virtual-device.bespoken.io/process?message="set the air conditioning to 21 degrees"&user_id=<your user id>&voice_id=Joey&language_code=en-US"

according to their documentation (https://read.bespoken.io/end-to-end/api/#http-api) which works if I curl it in my terminal.

Would that be possible?
How to proceed?
Thank you all in advance!