How to combine several regressions?

[Spellmen]

I'm working on a project to simplify procedures for collecting some temperatures with thermocouples. In the past, two TC have been used, and then the average of the two is the desired data. I am trying to use a TC in another location (easier to access, maintain, etc) to predict the average temperature of the other two. A typical cycle is about 18 hours, and I can easily use a least squares method to determine a regression equation for an individual cycle, but want to be able to use something like that universally.

I'm probably not explaining this well, but basically I have a bunch of similar regressions. Each regression is generated from, and can predict a single set of data. We have data and regressions from several sets now, and want to try and combine these regressions so we can simplify our procedures and use 1 regression to predict each test.

We basically have two temperature profiles, an average of two thermocouples in a hard to reach area, and then a third thermocouple positioned in a more accessible place. We’d like to use the temperature profile from the third thermocouple to predict the average of the other. The current regression is based on two parameters, time in the cycle, and temperature of the third thermocouple. The relevant profiles can be seen on the charts I linked.

If I have similar regressions like the ones below, with similar data, can I somehow combine them to form one prediction model? I’m not very savvy with statistics, so my only thought originally was to average the coefficients, but that can’t be right.

y = 300*time + 0.150*temp
y = 350*time + 0.120*temp
y = 337*time + 0.200*temp
chart

[m_the0ry]

Does a 'temperature profile' include temperature data points collected all the way through the coking cycle or just a single sampling of the temperature?

also, are you trying to estimate the entire curve or a single point?

[Spellmen]

[ QUOTE ]
Does a 'temperature profile' include temperature data points collected all the way through the coking cycle or just a single sampling of the temperature?

also, are you trying to estimate the entire curve or a single point?

[/ QUOTE ]

A datalogger takes a point every minute. I am trying to estimate the entire curve