Reading assignment: 20.7
If the temperature of a "black body" doubles, how much does its rate of
energy emission change?
The rate of energy emission is proportional to the 4th power of the temperature. So doubling the temperature will cause a 16-fold increase in power emission.
To decrease the energy lost by conduction from a hot object to a cold
one, what can you change?
Some ideas: decrease the contact area between the two objects, increase the path length of the heat flow, decrease the temperature difference, add an thermal insulator between the two.
Why do you think there are no equations in the "convection" section of the book?
Convection is a very complicated process and difficult to model precisely.