In both race cars and karts, an increase in tyre pressure will result in an increase in tyre temperature (with a few caveats and special cases). Any other reference you have read will almost certainly be referring to tyres used under normal road conditions.
With race cars and karts, we are concerned with the temperature of the contact patch, since this is the part that provides adhesion. With road cars, the concerns are ride comfort, fuel efficiency, load capacity etc. Road cars will generally see higher temps when lowering pressures because the contact patch isn't being worked hard enough, giving sidewall flex a greater contribution to tyre temperature.
Why does higher pressure result in higher temperatures? Many will tell you it's because of the resulting smaller contact patch. This certainly accounts for some of the affect, since temperatures across the width of the tyre indicate the smaller contact patch (higher temps toward the centre of the tyre, assuming sensible camber etc).
When you say you had to design the steering system, what exactly do you mean, and of what relevance is this to your questions regarding tyre temperatures. How involved were you in the design of the suspension system as a whole? Post your question over at the Autosport (Atlas F1) technical forum. You'll get an answer tailored to your specific requirements and lots of other useful info too.
Dave
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