Recent studies have led to speculation that solar‐terrestrial interaction, measured by sunspot number and geomagnetic activity, has played an important role in global temperature change over the past century or so. We treat this possibility as an hypothesis for testing. We examine the statistical significance of cross‐correlations between sunspot number, geomagnetic activity, and global surface temperature for the years 1868–2008, solar cycles 11–23. The data contain substantial autocorrelation and nonstationarity, properties that are incompatible with standard measures of cross‐correlational significance, but which can be largely removed by averaging over solar cycles and first‐difference detrending. Treated data show an expected statistically‐significant correlation between sunspot number and geomagnetic activity, Pearson p < 10⁻⁴, but correlations between global temperature and sunspot number (geomagnetic activity) are not significant, p = 0.9954, (p = 0.8171). In other words, straightforward analysis does not support widely‐cited suggestions that these data record a prominent role for solar‐terrestrial interaction in global climate change. With respect to the sunspot‐number, geomagnetic‐activity, and global‐temperature data, three alternative hypotheses remain difficult to reject: (1) the role of solar‐terrestrial interaction in recent climate change is contained wholly in long‐term trends and not in any shorter‐term secular variation, or, (2) an anthropogenic signal is hiding correlation between solar‐terrestrial variables and global temperature, or, (3) the null hypothesis, recent climate change has not been influenced by solar‐terrestrial interaction.