As jrwhit pointed out.
Your biggest issue will be the distance! Everything else can be over come.
You Don't state if the barn is on the same breaker panel.
There are a couple of ways to over come the distance issue.
Add a tm751 in the barn placing it up high and as close to the house as possible.
Also do a antenna mod to the Cm15A and place it as close to the barn and a high as possible! Send RF signals to the barn.
Another method would be to place a PC in the barn with a cm19 or another cm15 have
PcCompanion running on it no AHP needed.
(yes it can trigger events based on temperature)
You could add PCC in the house as well and use its Home networking option.
Of coarse that would be my last resort.
AHP will tell you it sent the command even if a third party software sends that info.
Having a light that turns on with the block heater would be the most accurate confirmation that the module received and acted on the signal.
As dave w stated:
If wire runs aren't to long powerline commands may work but you most likely would need a booster of some sort which I'm not familiar with.