Conduction, convection, and radiation are three basic modes of heat transfer which often exist together. However, it is up to now a challenge to simultaneously manipulate them within the framework of transformation theory because they possess diverse properties with different mechanisms. To solve this problem, we develop a transformation theory to control them simultaneously (herein called transformation omnithermotics). With the present theory, we further design three devices including omnithermal cloaking, concentrating, and rotating as model applications. Finite-element simulations and experimental suggestions are also provided to confirming these applications. This work not only unifies the three basic modes of heat transfer within the theoretical framework of transformation omnithermotics, but also provides novel hints and potential applications to thermal management.