BLE device directions
I propose you use a nordic nRF51822 chip that includes the temperature information in advertisement data with an advertisement period of 1 to 2 seconds. Use connectable undirected advertisements. If something wishes to connect to the temperature monitor, implement an appropriate temperature characteristic.

Bluetooth SIG Temperature measurement characteristic

Do not include a LED, this will ruin your battery life.
Is the LED REALLY needed? Do all the data processing on the host side.