# Thermal Modeling

I have an electronic assembly and part of what it does is to measure and report temperature. The electronics are housed is a plastic enclosure, and there is a small fan blowing out of the enclosure. There are also intake openings in the enclosure wall.

It's a simple fact that the temperature inside the enclosure is above ambient temperature seeing as the electronics itself is a heat source and the enclosure naturally has thermal insulating properties.

That being said I want to report ambient temperature without my temperature sensor being outside the enclosure, and I'm willing to perform a calibration step to get there.

The questions are, (1) is it sufficient to model the transform as a simple offset? (2) What tools can I use to understand the relationship between the internal and external temperature in my enclosure, over a range of external temperatures? (3) What are the most important variables I need to control in order for my calibration to hold in practice?

Provided the power dissipated in the box (or the energy consumed inside the box) is constant then the temperature rise, $\Delta T$ of the inside relative to the outside will be governed by the thermal resistance of the box inside to outside. This would be analogous to Ohm's law, $V = IR$ but now we have $\Delta T = QR$ where Q is the heat flow and R is the thermal resistance which in your case should be a constant.