Go to the Southeast Shrine.
From the Temple of Time, go south, then southeast toward the shrine. On the way, you can battle a Soldier Construct. Nearby, you can gather some Spicy Peppers. You can cook these in the nearby cookpot, either by themselves or with other ingredients, to make food that will give you temporary Cold Resistance when you eat them. These peppers don't give Cold Resistance until they are cooked, so be sure to make food with all of them.
From here, go southeast up the icy slope. You will soon be notified that it is too cold, so be sure to eat one of the cold resistance foods that you cooked.
Go south along the path and you will eventually find a Maker Construct. Talk to it, and if you don't have an Energy Cell, the Construct will give you one.
Jump onto the raft that is already in the water and hit the fan with your weakest weapon. After you reach the other side, be sure to hit the fan again to turn it off so it will stop using energy. Carefully jump off of the raft to avoid falling in.
You can optionally go south from here to find another cookpot, as well as more Spicy Peppers.
Otherwise, go north, and make your way up the stairs. Climb up the cliffs at the top, and when you reach a pond with a waterfall, walk southeast along the stone and you will go on a path behind the waterfall.
At the top of the path, cross the bridge over the water and battle a Soldier Construct on the other side. Then you can use the cookpot at the end of the path if you wish.
After that, go up the stairs and follow the path behind another waterfall. This leads to a part of the wall that is not icy, so you can climb it without slipping. Climb the non-icy wall, and when you reach a flat surface, be sure to wait for your stamina to refill before you go farther up.
At the top, you find another stone structure. There is a cookpot, and you will see some flint on the ground next to it. (If you lose the flint, just drop another on the ground next to the cookpot.) Hit the flint with a metal weapon to start the fire under the cookpot, and then you can use it to cook.
Go west from there to reach the shrine. Check on the glowing object to open the shrine, and go into the Gutanbac Shrine.