Whenever I've used neem oil I drench the plants until dripping. If you have to take it outside on a day to spray it I would. I would hose it down first and the clean off any trace of the mites before spraying . It should be warm enough that it could tolerate a brief amount of time in the 50s. Also, it won't be long before it can go out for good, so be patient.

Well, I just checked the label on my organicide and I did not see neem oil in the ingredient list it says sesame oil as main! What should I go and pick up or can I make a mix of soap, water? Should I treat the soil?

How often are you misting it? If you mist both sides of the fronds at least 2-3 times a week for a while you'll get rid of them. And after a few weeks you wont have to mist as much to keep them away. I had to do that to keep spider mites off my coconut palms.
And I agree with bradelyo. If you can you should take it outside and hose it down pretty good.

- US_Marine