Blue photons (= photons of ~420 nm wavelength) have higher energy than red ones (= photons of ~600 nm wavelength). That means that each individual absorbed blue photon will indeed heat the surface more, because it gives it more energy. But two red photons would heat the surface more than a single blue photon. Photons themselves don't "have" heat, heat is a collective consequence of random motion of many atoms/molecules/...
Photoelectric effect in the video is a bit different phenomenon from heating the material because photons need sufficient energy to eject electrons from the material. Red light might not eject any electrons no matter how many photons hit the material, while blue would even if you have few photons (and therefore lower heating).
Temperature of light, eg as on "3000K" light bulbs, is something different still. Blackbody gives out EM radiation. Spectrum of that radiation depends on the temperature - say something at 3000K has peak of radiation at approximately 1 micrometer wavelength (near-IR) while our sun at ~6000K has peak at green light. 184
And that temperature designation of the light bulb simply means "this bulb gives out light that has approximately similar spectrum to the body at this temperature" (skipping details about color quality).
You can start with 3000K bulbs, then add filter to get 6000K light. First light is red-ish, second one is blue-ish. But even though after filter your photons flying out are more blue and therefore have more energy on average, this filter absorbed (or reflected; in video filter absorbed light) quite a lot of energy - many red photons had to get blocked. So, average photon has higher energy, but total energy of all photons in the light is lower. Shining unfiltered red-ish light on thermometer would heat it more than shining filtered blue-ish light on it.
This losing energy is true even if you have laser light and convert it to have half the wavelength (eg 1064 nm to 532 nm) - in that case all input photons have low energy and all output photons have high energy, but you lost many (at least half) photons in the process, so the total energy (that gets converted to heat by absorber) is the same or usually lower (with some energy lost during conversion and resulting in heating of the converter). In this case of up-conversion (photons flying out having higher energy) you can also get photoelectric effect with the converted light while original one doesn't kick single electron out of the material. This is unlike with filters that merely block some wavelengths - there, photoelectric effect of filtered light is at most the same as in original light. 970