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Temperature compensation, expressed as the ability to maintain clock characteristics (mainly period) in face of temperature changes, that is, robustness, is considered a key feature of circadian clock systems. In this study, we explore the genetic basis for lack of robustness, that is, plasticity, of circadian clock as reflected by photosynthesis rhythmicity. The clock rhythmicity of a new wild barley reciprocal doubled haploid population was analysed with a high temporal resolution of pulsed amplitude modulation of chlorophyll fluorescence under optimal (22°C) and high (32°C) temperature. This comparison between two environments pointed to the prevalence of clock acceleration under heat. Genotyping by sequencing of doubled haploid lines indicated a rich recombination landscape with minor fixation (less than 8%) for one of the parental alleles. Quantitative genetic analysis included genotype by environment interactions and binary-threshold models. Variation in the circadian rhythm plasticity phenotypes, expressed as change (delta) of period and amplitude under two temperatures, was associated with maternal organelle genome (the plasmotype), as well as with several nuclear loci. This first reported rhythmicity driven by nuclear loci and plasmotype with few identified variants, paves the way for studying impact of cytonuclear variations on clock robustness and on plant adaptation to changing environments., (© 2019 John Wiley & Sons Ltd.)