Deriving integer and continuous values from Temperature (Simulated Annealing)

Hello

I would like to use the technique related to Simulated Annealing for my problem. Let's say I have an initial temperature T0 and I have 50 iterations.

At each iteration I would like to calcualte three values depending on the current temperature:

• An integer value: The value should start at 10 and increase to 100 in a way between linear and logarithmic.
• A continuous value: The value should start at 1 and decrease to 0 in a way between linear and exponential.

At each iteration the temperature can be either increased or decreased.

Which formulas are reasonable to use (or exists) for the increasing/decreasing of the temperature and for producing both values?