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What is the model number of the one you installed? Did you set the dip switches?
It can't come on if they are all off! What a dunce! Did they leave an instruction book for you for the unit and thermostat?
Are you sure it was an RJ-11 cord and not a phone cord?
They aren't interchangeable.....
And who is "they" here?
If the cord got hot it has a short and so something is wired up wrong.
Not too impressive......
Get the correct cord(s) first. If you got one hot then it was made wrong. Or else someone shipped you a phone cord instead of an RJ-11 cord. Did you change your mind about a phone chat?
I think you may need a good mobile tech to come and check this out. I will opt out of this and allow another tech to offer something if they can.