Any place along the Equator, as it has a constant temperature year round.
The warmest place in the USA in January is typically Miami, Florida, with average temperatures ranging from 60-77F.
The warmest places in Europe in January would be along the Mediterranean coast, such as Spain, Italy, and Greece.
In January, the warmest place in Greece is typically the southern region, particularly the islands of Crete and Rhodes. These areas benefit from milder temperatures due to their more southern location compared to the mainland.
In Europe at Christmas, the warmest place would be the Canary Islands. Temperatures would be in mid 50's to mid 60's in Fahrenheit.
The warmest place in the United States in January is typically found in southern Florida, specifically in cities like Miami and Key West. These areas experience milder winter temperatures compared to the rest of the country.
Coldest temperature for Iowa-47 degrees Fahrenheit Washta, Iowa January 12, 1912 Source: NOAA Website
January is one of the warmest months in Antarctica, which is as large as USA and Mexico combined. Temperatures over this vast continent vary, but at the South Pole, the temperature is about minus 30 degrees C, which is the warmest temperatures for that place in Antarctica.
Northeastern Europe is one of the coldest inhabited places on Earth. Southern Europe is the warmest place in all of Europe, so Northeastern Europe is most definitely not warmer than Southern Europe.
The warmest part of Europe right now is most likely Southern Europe (along the Mediterranean). This is the warmest part of Europe year round. However, it is pretty much warm all throughout Europe right now because it's summer.
The Mediterranean
The Mediterranean.
In the United States, the states that typically experience the warmest temperatures in January are Hawaii and Florida.