Study on strongly correlated electrons opened a new window so called gauge theory in modern condensed matter physics beyond the Fermi liquid theory and Landau-Ginzburg-Wilson framework. In this presentation we discuss heavy-fermion quantum criticality based on a gauge theory formulation from a slave-boson approach, where such a phase transition is driven by breakdown of Kondo screening, thus called the Kondo breakdown (KB) quantum critical point (QCP). Recently, this KB transition has been reinvestigated and identified with an orbital selective Mott transition [C. Pepin, Phys. Rev. Lett. 98, 206401 (2007)]. Based on this scenario, we discuss Gruneisen ratio and thermal transport at the KB QCP. A crucial point is that Kondo screening or hybridization fluctuations are described by z = 3 critical theory in an intermediate regime. Such critical fluctuations allow a diverging Gruneisen ratio with an exponent 2/3, consistent with an experiment, and lead us to predict a quasi-linear thermal conductivity with a logarithmic correction. In particular, both electrical and thermal conductivities are dominantly characterized by conduction electrons scattered with such hybridization fluctuations, thus Wiedemann-Franz law is predicted to hold at the KB QCP.