In this paper we develop an economic growth model that includes anthropogenic climate change. We explicitly include a research sector that creates new technologies and simultaneously expands productivities of existing technologies. The environment is affected by R&D activities both negatively, through increase of output from productivity growth, as well as positively, as new technologies are less harmful for the environment. We consider three different versions of the model. In the first version, there are no constraints with respect to research spending, while the R&D sector affects the rest of the economy. In this version, the environmental damages are lower than in the model with simple exogenous technical change. Next, we consider the research dynamics with a constant R&D budget set by the agent. We find that there exist two different steady states of this economy, one with higher productivities and less new technologies being developed, and the other with more technologies being created. In the last version, finally, we allow for dynamic R&D spending. For this version, it is demonstrated that sustained economic growth with preservation of the environment is possible given certain conditions as regards the technology and R&D spending.