PID algorithm for constant temperature controller.

Just what do you mean by

?

One PID algorithm is
Controller output = proportional gain P X error + integral gain I X ∫(error) + derivative gain D X d(error)/dt

 

The one thing you need to remember when trying to regulate a heating controller is the time lag through whatever you are trying to regulate. This lag can easily run into hours.

 

Slope of temperature curve during that first on-cycle should give a clue about process thermal capacity, and maybe that time lag mentioned by svein..

 

I'm not sure i understand that statement.
ONtime is (1-OFFtime).

You're mixing linear control with" on-off control" here, sometimes that's called "Bang-Bang control"
and the math of that is another world. I won't go there myself
From a quick search:
Here's a paper...
http://dimacs.rutgers.edu/Workshops/AIMS/slides/SLafrica4.pdf

and a couple references
http://en.wikipedia.org/wiki/Bang–bang_control
http://cds.linear.com/docs/en/datasheet/1041fa.pdf
http://liberzon.csl.illinois.edu/teaching/cvoc/node86.html

Your best bet is to keep your on-off intervals short compared to the process time constants and treat it as linear
or insert a PWM at your controller output.