Assuming your substance is a solid, then I believe your problem can be solved by applying a well known analytical solution for transient heat conduction in a semi-infinite solid.
If the substance is initially at a uniform temperature and the surface temperature is suddenly changed, then the analytical solution will provide the temperature at a given depth as a function of time.
Alternately, if your sample is small, or thin, and is heated uniformly on all surfaces (e.g., a ball bearing suddenly immersed in a heating or cooling fluid), then an analytical solution is available by using a well known transient lumped parameter approach. This method assumes that the entire mass is heating up uniformly.
If you are heating a fluid or gas, then additional physics must be included.
I can help you with the calculation and provide the equations if you can provie a few more details regarding the geometry, material type, and method of heating.
If you know the "Specific Heat Capacity" of your substance you can calculate as follows:-
Q= m*Cp*(t2-t1)
where Q = heat req in joules
m = mass of substance
t1 & t2 = intial and final temperatures of the
substance in Kelvin
further Power=Q/T
where Q is heat req in joules
P is power in watts
T is time in seconds
so assuming you know the power rating of your heat source you can transpose to find T time to heat your substance.
example
4kg of water requires heating in a kettle from say 293.15K
to 373.15K , specific heat capacity of water 4187J/kgK
the kettle has a power rating of 2000W
therefore Q= 4*4187*(373.15-293.15)= 1339840J
so to find the time to raise the water temp use P=Q/T
so T= Q/P = 1339840/2000 = 669.92 seconds or 11.165 minutes
Tremolo is correct - it's a transient problem. You need to know not only the specific heat, but the density and thermal conductivity. These three combined give you the thermal diffusivity. The time it takes to heat a given object depends on the shape of the object and the boundary conditions. For relatively simple shapes and boundary conditions, the differential equations can be solved to give a closed form solution, or possibly solved numerically - see books on heat conduction. For more complex shapes, you need FEA. Desertfox is correct about the amount of heat transfer required, however.
