# How to extrapolate partial curve based on other complete curves?

I heat a room to a certain temperature. Then I let it cool over time. I measure the temperature at 6 intervals as it cools. I repeat this process for some other rooms.

From this, I get a set of temperature observations of the same cooling process happening over time in different rooms:

Time interval:  0  1  2  3  4  5
--------------------------------
Room 1:        50 30 25 22 20 18
Room 2:        50 20 10  5  0  0
Room 3:        50 30 20 15 10  0

...

Room 100:      50 35 28 25 23 22


I heat a new room and let it start cooling. I take temperature readings at the first 3 time intervals (see purple line in graph).

How can I predict what the temperature will be at the next 3 time intervals in this room?

(I want to base these predictions on the first 3 temperature measurements I took in this new room, and on the measurements taken in other rooms.)