There are plenty of PCs that run 24/7 anyway.
But if you think electricity cost is at issue here, lets do some math.
Assume the jalapeno is 2.5W.
Average electricity cost in the US is 12¢/kWh. THats ~$2.5 per year. SO it takes 66 years before your electricity cost exceeds the purchase cost.
Or ~30 years if you use a raspberry pi to drive a single jalapeno.
At current prices, electricity cost is a non issue for these asics. If you have to worry about power consumption, it means you will never ever make a positive ROI on the purchase cost.