The power input is equal to the heat output minus any losses. One example of a loss is the slight heating of the conductors that carry the power to the heater - if the conductors are outside of the space of concern then you can't count that heat. Without a clear understanding of the problem at hand it's impossible to be more specific than that. The equation depends on the information you have to begin with.
The resistance of many materials changes with temperature. Over the long haul (weeks, months) heater materials can degrade so that there is a small change in resistance. Whether or not this is significant depends on the situation. In most cases the change in resistance with temperature is of significance. The change because of time is less significant and ignored in most situations.
The temperature will rise until equillibrium is reached - where the heat input to the system equals the heat output. In some situations equillibrium is reached quickly - or the conditions are considered acceptable quickly. In other situations this can be very tricky to model and predict. If the voltage is constant the heater is changing as it warms or cools so the power input is actually changing. If the power input is controlled then the heater output is actually changing - because the losses are changing. The conductivity of any insulating material changes with temperature.
Heat transfer can be very simple in some situations however it is actually quite the complex process. Share some more specifics and maybe we can help. As with other areas of science and engineering practitioners have developed methods to simply calculations where it's appropriate.