Milk

No matter how they pick, only the $1^\text{st}, 4^\text{th}, 7^\text{th}, 10^\text{th}$ can be the last cup of milk. This is because the numbers of cups on their left and right is divisible by 3, hence can be removed.

This problem reduces to fighting over 4 cups with temperature - $(1, 7, 8, 2)$ . Alice play first, and since she wants her milk to be as warm as possible, she removes the milk with temperature $1$ . Then Bob removes the milk with temperature $8$ . Finally, Alice removes the milk with temperature $2$ and all they left is the milk with temperature $7$ .

This is one solution in python:

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def solve(cups, player):
    "Milk"
    if len(cups) != 1:
        if player== "Alice":
            return max( solve(cups[0:k] + cups[k+3:len(cups)], "Bob") for k in range(len(cups) - 2))
        else:
            return min( solve(cups[0:k] + cups[k+3:len(cups)], "Alice") for k in range(len(cups) - 2))
    else:
        return cups[0]

print (solve([1,3,3,7,9,1,8,4,5,2], "Alice"))

Alice wants the milk to be as warm as possible Looking at the initial line, the three consecutive cups with the least sum are the first three: 1, 3, 3; leaving 7 9 1 8 4 5 2

Bob wants it coldest and should remove the set of three consecutive cups with the highest sum = 9 1 8,

leaving 7 4 5 2 Alice's turn: removes the 3 with the smallest sum = 4 5 2 Leaves 7

You might be able to argue that it would be better for Bob to leave the '1' and remove a different set of 3 Say he removes 8 4 5, that leaves 7 9 1 2, which still leaves Alice with the 7.

No matter what Alice removes, in fact, Bob can take out the 9 and 8 on his turn, leaving 7 the best Alice can do. Bob can only end with colder than a 7 if he can remove the 7, 8 and 9, which would require Alice to not play optimally.

First statement was removing 3 consecutive cups... Alice will remove the first three 1,3,3 Bob will remove 8,4,5 and we have to merge the rest. Do think of 8,4,5 you will come to know, no other consecutive options will suit for Bob. So now we are left with 7,9,1,2 Alice now will remove 9,1,2 as he wants his cup as hot as possible.

Thus we are left with only 7..