Another Simple Heat Loss Question

[TheH]

I'm trying to size (in watts) a heater to heat a glass of water from ambient (Ti) to a certain temperature (Tf) in a given time period (say, 1 hour).

The heat-loss from the glass at Ti is 0 watts.
The heat-loss from the glass at Tf is Y watts.
I'm assuming that the heat loss increases linearly between Ti and Tf (I hope this is reasonable).
The energy needed (assuming no heat-loss) to heat the water from Ti->Tf in 1 hour is X watts.

Naturally, I can size the heater to be (Y + X) watts. However, this will heat the water up faster than necessary because initially there will be no heat-loss from the glass.

Is there a clever way to more accurately size this heater?

Thanks for your time.

 

[TheH]

Note that here it is possible for X to be much larger than Y (when I want to heat the water up rapidly) and Y to be much larger than X (when I want to heat the water up slowly).