All light carries energy
You're completely right about that all forms of electromagnetic radiation carries energy, and you can refer to Bob's answer for the technical details. It's also quite false that only infrared radiation will heat things, but there's some truth hidden in the common misconceptions, so let's break things down.
I'm going to be talking about what how various frequencies (and their corresponding wavelength) interact with your body, and where they might come from.
My figures will be approximate, as I'm trying to convey an idea what's happening, not exact values or names.
Radio waves are really quite a broad term, ranging from waves of just a few Hz, up into the GigaHerz. Let's start at the low end.
Very long radio waves
At frequencies up to 1 kHz, your wavelength is at least 300 km (300 Mm/s / 1000 /s). That means your body is completely insignificant compared to the wave passing over it. It barely interacts with it at all. Interacting with these efficiently requires something with a size on the order of a planet. The main natural source of them is lightning strikes.
Still long radio waves
Jumping up several orders of magnitude, up to 1 MHz, the wavelengths are still at least 300 m. Your body still doesn't really interact with it, being more than 2 orders of magnitude smaller.
Shorter radio waves and microwaves
Going up to 1 GHz, we're starting to enter the realm of microwave radiation, though calling them radio waves is still correct. The wavelengths can get as short as 0.3 m (30 cm), and we're not far from the frequency of the typical microwave oven (2.45 GHz, with a wavelength of about 12.5 cm).
As you go through this frequency range, they start to interact with human bodies more and more. You might have noticed how the signals of TV and radio are affected by your mere presence near the antenna. The amount of energy involved tends to be rather low though, and when they interact with you, the energy deposited is distributed all over your body, so you won't feel it on your skin.
Going up to 1 THz, the wavelength shrinks down to .3 mm (300 $\mu m$). Used mainly for high-bandwidth wireless communication and radar, this starts to enter the range of frequencies that interacts mainly with your skin, and you will actually feel. The story goes that using microwaves for heating food was
discovered by a radar engineer whose chocolate bar melted when he walked in front of an antenna. That's at a very high power level though, and you won't normally encounter those outside of a microwave oven.
The cosmic microwave background is at 160 GHz, and is a blackbody emitter at about 3 Kelvin.
I'm slowing down our steps a bit now, as a lot of interesting changes are starting to happen.
For our purposes, we'll define "far infrared" as everything up to 100 THz (wavelengths down to 3 $\mu m$).
Like short microwaves, these will interact with your skin, and unlike microwaves, the black-body temperatures associated with these go up to about 80 degrees Celsius, beyond human body temperature.
As black-body emission goes up by the fourth power of temperature, this starts to involve significant amounts of energy, and this is where you start feeling the presence of warm things.
As this range also includes most of the temperatures we normally encounter, thermal cameras use it.
All in all, it's not strange that it's frequently called "thermal infrared".
Medium and Near infrared
Not all that much changes as the frequency increases to 430 THz (700 nm), except the black-body temperatures go up to around 4 kilokelvin and the radiative energies involved continue increasing by the fourth power of the temperature. This is the stuff you feel when near a fire, or an incandescent lightbulb.
Part of this range is used for thermal cameras that are intended to track high-temperature heat sources, typically the heat engines that power tanks, jets and rockets.
Going up to 750 THz, the wavelength continues to decrease to about 400 nm. Not all that much changes compared to near infrared, but there are some notable points.
- About half the solar energy that reaches the surface of the earth is in this range, similar to the amount of infrared energy.
- It's absorbed by the skin similarly to infrared. It's certainly not the case that this is an entirely different kind of radiation.
- The black-body temperatures involved are similar to those of the surface of stars, which is why the colors of stars mostly span this range.
- The photon energies are beginning to get large enough (on the order of 1 electron-volt (eV)) to do interesting things. This, along with the fact that the atmosphere is very transparent in this range, allows for things like light receptors and eyes. (infrared 'eyes' tend to use localized heating for sensing, which requires much larger "pixel sizes")
Ultraviolet is named such because it's beyond violet: we can't see it. As the frequencies increase, more things start to change.
Up to 1 PHz (300 nm), humans may not be able to see it, but that doesn't mean other animals can't.
Beyond 1.5 PHz (shorter than 200 nm), atmospheric absorption increases suddenly, as the photon energy becomes high enough to ionize oxygen. At even higher frequencies, they will also interact with nitrogen.
As the photon energy increases, the number of molecules the photons can break increases, increasing the potential for damage and sunburn, though no ultraviolet light appears to be entirely safe.
The sun's light output in ultraviolet drops off fairly quickly, as we exceed its black-body temperature.
Ultraviolet light is still mostly absorbed by the skin, but if your skin feels warm due to ultraviolet radiation, you'll get a terrible sunburn in a hurry.
Once we exceed 30 PHz (10 nm), we cross the rather arbitrary threshold into
X-rays start 'soft', meaning they don't penetrate much, and are strongly absorbed by air, but as frequencies increase, wavelengths get shorter and photon energy increases. Around 10 keV (120 pm, 12.5 EHz), penetration depth starts to exceed 1 mm, crossing into "Hard X-Ray" territory. Hard X-Rays will penetrate deeper, allowing them to do distribute their energy beyond your skin. Again, if you feel heating effects from this, you should be worrying about the lethal dose of ionizing radiation you just received instead.
The difference between X-Rays and Gamma Rays are their origin: X-Rays are generated using electronic processes, while Gamma Rays are generated using nuclear processes. Their energy ranges overlap, but a typical Gamma Ray photon might be at 300 EHz (1 pm, 1.25 MeV). They behave similarly to hard X-Rays, but at higher energy, more so.
All light carries energy, but in the typical human experience, only infrared and visible light will be felt as heating you significantly. The visible light will also typically be accompanied by infrared light, so it's not strange to assume that the heat is carried (only) by the infrared light.
However, if you walk out in the sun, and feel its 1 kW/m^2 irradiance, about half the energy heating you is actually visible light, not infrared.
Also, if you use a thermal camera, you're actually measuring a specific band on infrared light, and there are several such bands depending on what you're looking for. (animals and their environment, or the exhaust of heat engines)