Differences between a planar coil and coplanar waveguide to create a local 1D AC magnetic field
You're going to see a lot of differences between a standard cpw and a planar microcoil.  The bandwidth and Q will make tuning for your transmission frequency difficult, especially over 1 GHz to 5 GHz.

Field spectrum?  Do you mean radiation pattern at different frequencies?

For higher power you'll probably need several in a phased array.  If you gave us a better idea of what you are doing with it, we could help.  You mention heat being a problem, is this an MRI application?  But yes, inductance will vary strongly over frequency and heat.