Is there a way to calculate the ground and 10m temperature from standard 2m temperature measurements?
There is an equation for a model of vertical variation in air temperature 



It unifies concepts from a whole range of sciences. You will need to know the sensible heat flux H from the respective surface (which can be calculated as a result of the energy balance of where you are). Further you can calculate the volumetric specific heat capacity pc(p) of air, which is approximately 1.2 kJ/(m³ K) and relate it to the shear velocity or friction velocity of your surface. This is finally related to the logarithmic measure of the term (z-d)/zH where z is the height of which you want to know the temperature and d is the zero plane displacement. zH finally is the Roughness of your surface. 

This has to do with the fact, that heat transfer over surfaces usually is turbulent and not just determined by vertical convection. I recommend you to take a look at Campbell &amp; Norman "An Introduction to Environmental Biophysics" (1998). It's a very comprehensive book and treats all the mentioned concepts. 

I'm working on a basic computation of this at the moment but it still needs a little time. Once it's done, I'd be very excited to see if it actually is able to model the measured temperatures. I'll keep you updated on how it's going.