The spin Peltier effect (SPE) induced by the spin Hall effect has been investigated in Pt/yttrium-iron-garnet (YIG) junctions by the lock-in thermography technique. First, we propose and demonstrate a new method enabling systematic measurements of the charge-current angle dependence of spin-caloritronic and thermoelectric phenomena, confirming the symmetry of the SPE. Then, to investigate the temporal response of the SPE, we measured the charge-current frequency dependence of the spin-current-induced temperature modulation in a wide frequency range. The SPE signals are found to be almost independent of the frequency up to 100 Hz although the Joule-heating signals in the Pt layer are strongly dependent on the frequency, indicating that the spin-current-induced temperature modulation reaches the steady state in a much shorter time than the conventional heating effects. The experimental methods and results reported here will be useful for clarifying mechanisms and behaviors of spin-caloritronic and thermoelectric phenomena.