There is this formula which indirectly relates watts to degrees, it just requires some other variables as well:
ΔQ = mcΔT
Where Q is the energy in Joules (converted from watts--again, a few other variables are needed), m is the mass, c is the "specific heat" (amount of heat required to raise the temperature of a material by one unit of temperature, relative to another material) of the substance that is being heated, and T is the temperature in Celsius. And of course, Δ is 'delta', meaning 'change'.