Why do people always jump to ESP8266 or WIFI modules for transmitting a few bits every 10 minutes?! Sure you can power it down afterwards, but its overkill. Whilst you could do the maths to calculation power budget for ESP8266 - its faster over-the-air-rate means its powered up for less time - there's also the time it takes to connect to the network. Yes, using the ESP8266 allows for two way communication, over-the-air updates, and direct interaction via a webpage, but if one is making 10-20 of these things *just* for measuring small sensors the cost will add up, and they will drain batteries.
Any 8-bitter will do - Arduino just seems to be the most accessible, and some $2 433MHz Modules, which can be powered from an MCU IO. The only downside with Arduino's is power consumption. If you use a stock Arduino its regulator will eat power, and it generally isn't geared for low-power, but you can put the MCU to sleep. An Arduino pro mini with the regulator jumper removed would probably be the easiest and cheapest setup.