The interplay between spin transport and thermoelectricity offers several novel ways of generating, manipulating, and detecting nonequilibrium spin in a wide range of materials. Here, we formulate a phenomenological model in the spirit of the standard model of electrical spin injection to describe the electronic mechanism coupling charge, spin, and heat transport and employ the model to analyze several different geometries containing ferromagnetic (F) and nonmagnetic (N) regions: F, F/N, and F/N/F junctions, which are subject to thermal gradients. We present analytical formulas for the spin-accumulation and spin-current profiles in those junctions that are valid for both tunnel and transparent (as well as intermediate) contacts. For F/N junctions, we calculate the thermal spin-injection efficiency and the spin-accumulation-induced nonequilibrium thermopower. We find conditions for countering thermal spin effects in the N region with electrical spin injection. This compensating effect should be particularly useful for distinguishing electronic from other mechanisms of spin injection by thermal gradients. For F/N/F junctions, we analyze the differences in the nonequilibrium thermopower (and chemical potentials) for parallel and antiparallel orientations of the F magnetizations, as evidence and a quantitative measure of the spin accumulation in N. Furthermore, we study the Peltier and spin Peltier effects in F/N and F/N/F junctions and present analytical formulas for the heat evolution at the interfaces of isothermal junctions.