How does anthropogenic heating affect global warming?
A recent study by Chen et al. (2014) in the article Anthropogenic Heat Release: Estimation of Global Distribution and
Possible Climate Effect defined the heat release as you described as being Anthropogenic heat release (AHR), and has it basis as a product of economic prosperity, which leads to energy usage and excess heat produced - usually in large cities globally - this is sometimes referred to as 'waste heat'.

In their research, Chen et al  report on an earlier global estimate made by Chen and Shi, 2012:


Globally, the estimated AHR is 0.03 Wm$^{-2}$
Over land, this average becomes 0.10 Wm$^{-2}$


Although, globally, these amounts are considerably less than that from $\ce{CO2}$ emissions, they still add to the problem - especially as the rate of urbanisation, hence the use of heat generating appliances is increasing rapidly, this value will become more significant.

However on a regional scale, over large cities for example, such as Tokyo, the effects of AHR are more profound.  In and around the region around Tokyo city, the AHR can exceed 400 Wm$^{-2}$.  So what are the consequences of this flux?  Most of it causes regional effects, in particular (from Chen et al.):


Can influence urban climates and is a significant contributor to the urban heat island, which amongst other things can affect regional rain patterns.
Can affect the dynamics and thermodynamics of urban boundary layers.
Can influence the reaction rates and types of emitted aerosol and particulate species.


All of which have a compounding effect in the regional and to a lesser degree, global environment, that Chen et al. attribute to as being a cause of a 1-2K temperature rise in high altitude areas in Eurasia and North America and as a disrupting influence in global atmospheric circulation.

Edit 28/2/2016: There is an interesting blog post about a similar phenomenon: Dubai construction alters local climate

Additional references

Chen, B., and G.-Y. Shi, 2012: Estimation of the distribution
of global anthropogenic heat flux. Atmos. Oceanic
Sci. Lett., 5, 108–112.