Assuming there is no heat loss to the atmosphere and initially the water temp is below the cheese melting point.
Q1 + Q2 = Q3 + Q4 + Q5
Q1 = heat given by steam condensing
= m1*L1
Q2 = heat given by condensed water cooling from 100 deg.C
to T1
= m1*c1*(100-T1)
Q3 = heat taken by...