In this paper, the self-organizing inductive methodology is applied for the non-anticipative analog forecasting of the heat/cold waves in the natural environment subsystem of the smart city. The prediction algorithm is described by two paradigms. First one (short range) uses quantum computing formalism. D-Wave adiabatic quantum computing Ising model is employed and evaluated for the forecasting of positive extremes of daily mean air temperature. Forecast models are designed with two to five qubits, which represent 2-, 3-, 4-, and 5-day historical data, respectively. Ising model’s real-valued weights and dimensionless coefficients are calculated using daily mean air temperatures from 119 places around the world as well as sea level (Aburatsu, Japan). The proposed forecast quantum computing algorithm is simulated based on traditional computer architecture and combinatorial optimization of Ising model parameters for the Ronald Reagan Washington National Airport dataset with 1-day lead-time on learning sample 1975-2010 yr. Analysis of the forecast accuracy (ratio of successful predictions to total number of predictions) on the validation sample 2011-2014 yr shows that Ising model with three qubits has 100% accuracy, which is significant as compared to other methods. However, number of identified heat waves is small (only one out of nineteen in this case). Second paradigm (long range) uses classical computation in the Microsoft Azure public cloud. Here, the forecast method identifies the dependencies between the current values of two meteorological variables and the future state of another variable. The method is applied to the prediction of heat/cold waves at Ronald Reagan Washington National Airport. The data include the above-stated datasets plus monthly mean Darwin and Tahiti sea level pressures, SOI, equatorial SOI, sea surface temperature, and multivariate ENSO index (131 datasets in total). Every dataset is split into two samples, for learning and validation, respectively. Initially, the sum of the values at two different locations (minus corresponding expectation values) is calculated with lead-time from 14 to 365 days on summation interval of length from 1 to 365 days. Objective function defines the distribution based on two input datasets with appropriate lead-time and summation interval, which have maximum (or minimum) sum compared with the rest of data four times at least (with a minimum time difference of at least 30 days) when extreme event occurs on the learning sample. Specific extreme events at Ronald Reagan Washington National Airport were thus predicted on the validation sample, based on rules referring to events in earlier years. Some extremes are specifically predicted (up to 26.3% of all extremes). The methodology has 100% forecast accuracy with respect to the sign of predicted and actual values. Nowadays, the smart city project is developed at School of Engineering and Sciences (San Luis Potosi), Tecnológico de Monterrey. The early warning of heat/cold waves as well as technical aspect (remote control with Arduino Ethernet Shield and virtual power plant with solar energy are emphasized) are the focus of the Internet of Things project.