Hi, welcome to the forum.
Often three AA batteries are used. The 8MHz 3.3V Pro Mini can still run at 5V.
With rechargeable NiMH batteries, it will be 3 * 1.2 = 3.6V.
What is the voltage after charging ? About 1.25 V ? then it will be 3.75V.
If the Pro Mini is in sleep-mode most of the time, then it should run for more than a year.
The voltage for the Nordic nRF24L01+ is 1.9 to 3.6V. If you buy a cheap NRF24 module, then it has probably a counterfeit chip. Maybe those counterfeit chips only work at 3.3V.
Which temperature sensor is it ? It is a module ? which module ?
Can you show a photo of your project ?