No study of coping with climate change is complete without considering geoengineering. Leveraging Tsiolkovsky's and Tsander's 1920s idea to use mirrors for space propulsion, Fuller's 1940s Dymaxion Grid, Glaser's 1970s study of solar power satellites, and Forward's 1970-90s concepts of "statites" and "Starwisps", we propose placing one or more large (Σarea=700 K km2) lightsail(s) in a radiation-levitated non-Keplerian orbit(s) just sunward of the Sun-Earth Lagrange-1 point. The purpose of this syncretic concept is twofold: (I) As a parasol, it would reduce insolation on Earth by at least one-quarter of a percent, same as that which caused 1.8 °C drop during the "Little Ice Age" (∼1550-1850), and same as the IPCC Third Report's mid-range value for global warming by 2050. Lowering temperature will reduce the atmosphere's water vapor content, which should reverse the increasing frequency and severity of storms, likewise reducing the damage accompanying climate change. It transforms the "solar constant" to a controlled solar variable. The sail would utilize the very photons it diverts from us to maintain its position without expensive fuel. (II) As a ∼100+ K km2 photovoltaic power station, the parasol could displace over 300 EJ/a (∼100 trillion kWh/yr) of fossil-fired electricity for its creators, roughly the entire global demand forecast by 2050, in turn displacing most carbon burners from the terrestrial grid, providing US$trillions in revenue from clean energy sales to amortize the scheme. This approach to geoengineering is not precluded by international treaty, but it is not a panacea either because it does not fix the other consequences of exponentially growing combustion of fossil fuels. However, it would buy time because it is self-funding ("pay-as-you-go"); furthermore it is linear, scalable, minimally intrusive, and above all, reversible. If Tellurian spacefaring civilization bootstraps its exponential growth with lightsails, there might eventually be enough of them to have a detectable effect on Sol's apparent luminosity as seen from far away, similar to the eponymous Dyson Sphere. So we tagged our concept with the moniker "Dyson Dot".