> 1) heat a to the temperature I want b to be heated up to and 
> then keep a constant there until b reaches the same temperature

I don't see why you need any calculations... This option will bring b up to
temp at a rate dependant on the mass of b and the insulation between the two
assuming they are both mixed to uniform temperature inside. The temp graph
in b will be a curve which will flatten out as b approaches the target
temperature. It will never /actually/ reach the target but will come very
close.

> 2) heat b to a higher temperature than I want b to be at and 
> then let it cool down while b heats up with the heat given 
> off by a until eventually both reach the same temperature

We assume this should have started with "heat /a/ to a higher..." 

This one depends on the ratio of masses between a and b and the
insulation... And the mixing...  The curve will be steeper at first and then
flatten out again. Same problems.

3) heat b to a temperature that is x degrees above a and keep increasing b
until a hits the target then remove b. This one will give you a straight
line temperature increase which will make it easy for you to predict when
the target will be reached and adjust x accordingly on the fly. "A" WILL
reach the target temp, and will probably overshoot it slightly unless you
can remove b instantly.

Feedback removes variables.

---
James.
 

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