Consider that the global average land+sea temperature for this month (February), averaged over the entire 20th century, was 12.1 C. In a chaotic system, one would expect a roughly equal probability of seeing a cooler temperature as a hotter one, individually or averaged, though the average of large numbers of readings are less likely to show outliers. Seasonal and other cyclical factors would skew temperatures one way for a while, then the other way, balancing out over time.
For 2015, the globally-averaged temperature for February was 0.86 C higher than that 20th century average. If that was a single reading, or a local average, that wouldn't be at all noteworthy. Even averaged across the entire globe for the month, it was merely the second-highest February recorded, next to 1998. Similarly for land-only average temperatures, though with larger variations.
But when you consider that 2015 was the 30th hotter-than-average February in a row, the odds shift dramatically. If there's a 50/50 chance that we would see a hotter-than-average February any given year, then there's 1 chance in 2^30 that we would get 30 hotter "heads" in a row - ridiculously improbable. There hasn't been a cooler-than-average February since 1985 - and February 2016 was even hotter, setting a new record at 1.21 C above the average. Clearly the global average temperature isn't stable, but is showing a long-term underlying rising trend, which makes the new highest-temperature-ever records not only more likely, but bound to happen eventually. (Incidentally, if you use yearly averages instead of just February, it's now been 38 years of above-average temperatures.)
So the existence of a rising temperature trend is virtually certain. Whether it's anthropic or caused by a hitherto-undiscovered long-term natural cycle is a separate discussion, but the probability of the former is very high indeed.