homebrewing hard cider

I'm attempting to home brew a hard cider, starting with the simplest possible recipe. 
Ingredients:

5 gallons of apple cider - no preservatives, UV pasteurized (not heat)
1 packet (5 g) champagne yeast
1 tsp sugar
1/2 cup warm water

What I did:

• sterilized fermenter, airlock & stopper, thermometer, funnel
• prepped the yeast by mixing it with warm water and sugar
• warmed up the apple cider 
• fit 4 gallons in my pot, heated to ~92 F
• transferred the warm cider to the fermenter
• added the prepped yeast
• added the 5th gallon of cider that was still cold
• capped with the airlock

I could only fit 4 gallons of cider in my pot, so I heated that to a temperature above where I wanted it such that by adding the 5th cold gallon the final temperature would be approximately 75 F.  Equation I used was in Kelvin:

(x * 4/5) + 273 K = 297 K

where x is the temperature needed to heat to.  Solving for x:

x * 4/5 = 24 DK

x = 30 DK

The temperature needs to be 30 "delta-Kelvin" above 273, which is 86 F.  I ended up heating to 92 F in actual practice.

One thing I should have done probably is sterilize the pot I heated the cider in - I don't normally do this because I'm boiling the liquid in it, but that is not what I did this time.