||The characterization of submesoscale dynamics is crucial to apprehend their impact on the global ocean properties. Direct measurements of fine structures over the world oceans, nevertheless, are at present severely limited by the spatial resolution of available satellite products. In this work we numerically investigate the possibility to reconstruct tracer fields, like surface temperature, at small scales, from low-resolution data using a Lagrangian technique based on the properties of chaotic advection. The capabilities of the method are explored in the context of a forced surface-quasigeostrophic (SQG) turbulent flow representing a large-scale meandering jet and smaller-scale eddies. Both qualitative and quantitative comparisons are performed between the original (high-resolution) fields and their reconstructions that use only low-resolution data. Good agreement is found for filamentary structures, even in the presence of a large-scale forcing on the tracer dynamics. The statistics of tracer gradients, which are relevant for assessing the possibility to detect fronts, are found to be accurately reproduced. Exploiting SQG theory, the reconstruction technique is also extended to obtain the velocity field in three dimensions when temperature is the tracer. The results indicate that relevant features of dynamical quantities at small scales may be adequately deduced from only low-resolution temperature data. However, the ability to reconstruct the flow is critically limited by the energetic level of submesoscales. Indeed, only structures generated by non-local mesoscale features can be well retrieved, while those associated to the local dynamics of submesoscale eddies cannot be recovered.