Complex sentence: Keeler's subsequent affair with Profumo went on at a time when she was also sleeping with Ivanov, heightening Cold War tensions that were already magnified as a result of the Cuban Missile Crisis.
Split into simpler sentences: Keeler's subsequent affair with Profumo went on at a time when she was also sleeping with Ivanov. This was at a time when Cold War tensions were getting hotter as a result of the Cuban Missile Crisis.