Subject: Can I measure heating of earth's core due to solar wind/magnetic field/CME?

Is there possible heating of the Earth's core from induced current created by 
passage of the Earth through the Solar Wind,Magnetic field, or impacts with 
CMEs?
 
Question 1:
While I realize most heating within the core is believed to come from 
radioactive decay of Uranium and Thorium, even a tiny amount of heat generated 
by these induced currents would amount to a measurable amount over 4.5 billion 
years.  How do I calculate this?
 
Question 2:
How long does it take for any heat from the Earth's core to affect/reach the 
Mantle/surface?
 
It seems to me that small induced current from Solar activity (Magnetic fields, 
solar wind, Plasma Fields, Coronal Mass Ejections, etc) over billions of years 
must add up to a significant and measurable sum.  Calculating the effect on 
Earth's Core temperature is confusing and difficult.

Re: Can I measure heating of earth's core due to solar wind/magnetic field/CME?