Can temperature influence your circadian clock? The answer is: probably. There is some intuition to it, given that environmental temperature itself follows a daily cycle. Yet, there are very few studies on its effect on human circadian rhythm.1
Effects in mammals
Temperature has been shown to be a zeitgeber (i.e. able to shift circadian rhythm) for mammals, but with mixed results:1,2 In a study with mice by Refinetti et al.,1 1h of cold per day was shown to be a little inferior in its effect than 1h of light (65% vs. 95% of mice affected). However, according to the authors, the difference was not significant if mice with suboptimal exposure due to the study setting were excluded from analysis.
In another study, only 45% of squirell monkeys exposed to periodic cycles of warmth and cold under constant darkness synchronized their circadian clock with temperature.2 Pálková et al.5 suspect that the zeitgeber strength of temperature correlates with the amplitude of changes in core body temperature in animals. Following this hypothesis, temperature would only be a weak zeitgeber in humans.
A study with rats showed that the circadian phase response curve to heat was similar to that for light, resulting in a clock advancement in the first half of subjective day and a delay at subjective nighttime.3
A human study
When it comes to humans, it has been shown that a sequence of slow linear decrease and increase in ambient temperature during sleep could advance the point of minimum core temperature by an astounding 143min.4 However, while the point of minimum core temperature is a marker for circadian time, this might have been an acute response to the temperature change and not a shift, as core temperature of the subjects was not measured in the days after the intervention and no other marker for circadian time was examined.
To conclude, temperature may influence your circadian rhythm, but likely with a weaker strength than light. Timing for advance and delay is similar to that of light. A combined application, as it comes naturally by the sun, therefore seems to be a good idea.
 Refinetti, R. (2015). Comparison of light, food, and temperature as environmental synchronizers of the circadian rhythm of activity in mice. Journal of Physiological Sciences, 65(4), 359–366. https://doi.org/10.1007/s12576-015-0374-7
 Aschoff, J., & Tokura, H. (1986). Circadian Activity Rhythms in Squirrel Monkeys: Entrainment by Temperature Cycles 1. Journal of Biological Rhythms, 1(2), 91–99. https://doi.org/10.1177/074873048600100201
 Francis, A. J. P., & Coleman, G. J. (1997). Phase response curves to ambient temperature pulses in rats. Physiology and Behavior, 62(6), 1211–1217. https://doi.org/10.1016/S0031-9384(97)00202-3
 Dewasmes, G., Signoret, P., Nicolas, A., Ehrhart, J., & Muzet, A. (1996). Advances of human core temperature minimum and maximal paradoxical sleep propensity by ambient thermal transients. Neuroscience Letters, 215(1), 25–28. https://doi.org/10.1016/S0304-3940(96)12936-0
 Pálková, M., Sigmund, L., & Erkert, H. G. (1999). Effect of ambient temperature on the circadian activity rhythm in common marmosets, Callithrix j. jacchus (primates). Chronobiology International, 16(2), 149–161. https://doi.org/10.3109/07420529909019082