I don't think you need a heat lamp, just straw or wood chips, they have lots of down and can easily handle the cold. Mine have a choice and prefer to stay outside! I have livestock dogs though, so I don't have to worry so much about predators.
As to your electric fencing, we bought, several years ago, a pet fencer to keep one of our house dogs from digging under the fence. We ran a wire a few inches off the ground a few inches away from the fence. The pet fencer was cheap, only $20 or $25 and kept that 60 pound dog well away from the fence! I think it would be fine for what you need. It isn't big enough for huge acres and acres for huge animals like horses or cows, but for small animals and small areas, it works great. We got ours at Tractor Supply.
As to your electric fencing, we bought, several years ago, a pet fencer to keep one of our house dogs from digging under the fence. We ran a wire a few inches off the ground a few inches away from the fence. The pet fencer was cheap, only $20 or $25 and kept that 60 pound dog well away from the fence! I think it would be fine for what you need. It isn't big enough for huge acres and acres for huge animals like horses or cows, but for small animals and small areas, it works great. We got ours at Tractor Supply.