How does one convert

FROM

the rate of heat transfer

Q = BTU/hr (calculated from Q = -k * A * (T2 - T1)/x, where T2 < T1 (initially); x is the width of the conducting material, and A is the conduction area)

TO

the rate of temperature change

F/s, where F is degrees Fahrenheit and s is seconds.

The larger problem I'm trying to solve is:

Once a heat source of temperature T1 is applied to one side of a metal sheet of thickness x, how long does it take the other side of the sheet with initial temperature T2 < T1 to reach the same temperature T1?

Also, it seems there would be a way to convert the temperature T for a given volume of water to its heat content in BTU's? Does one have to know or assume an initial temperature T0?

Thanks in advance for your help