Combined heat and power (CHP) plants are main generation units in district heating systems that produce both heat and electric power simultaneously. Moreover, CHP plants can participate in electricity markets, selling and buying the extra power when profitable. However, operational decisions have to be made with unknown electricity prices. The distribution of unknown electricity prices is also not known exactly and uncertain in practice. Therefore, the need of tools to schedule CHP units' production under distributional uncertainty is necessary for CHP producers. On top of that, a heating network could serve as a heat storage and an additional source of flexibility for CHP plants. In this paper, a distributionally robust short-term operational model of CHP plants in the day-ahead electricity market is developed. The model accounts for the heating network and considers temperature dynamics in the pipes. The problem is formulated in a data-driven manner, where the production decisions explicitly depend on the historical data for the uncertain day-ahead electricity prices. A case study is performed, and the resulting profit of the CHP producer is analyzed. The proposed operational strategy shows high reliability in the out-of-sample performance and a profit gain of the CHP producer, who is aware of the temperature dynamics in the heating network.