As already stated by others, @ 2 GHz is water a much better absorber then gold. Gold is in the other end of the scale, a low loss metal and a good reflector. Nano scale does not change that to the better from your view.
Thin gold foil is used as heat reflector, for example is such foil used as blankets to keep people warm at accidents (reduce body temperature loss) so gold does not absorb heat well in IR/Red wavelengths. Bad news that it is hard to heat gold, if the idea was to heat gold in water, without heating any water.
By using a very strong magnetic or electric field for induced heating in near field, yes that works for any metal, it is commonly used for melting metal at foundry's. Limitation factor is that the metal melting pot must have reasonable size or enough electric loss compared to frequency wave length. At 2 GHz is it however not really nano size. A lot of bad news now.
It is also possible to make an electrolytic solution if ratio of gold ions relative fluid solution is big enough. It will result in a kind of heating due to chemical movements of these ions. Result is still radiated heating in IR range due to friction and gold will probably have a slower temperature raising then the fluid around it.
In short, your requirements are killed by rather basic knowledge.
Any method, it is a good idea to use deionized water and very pure gold surface.
A classical test to prove this is to heat two glasses of water in a microwave oven, one half filled with regular drinking water and one glass half filled with deionized, desalinated water. Place them both at good distance from each other in the oven as they else will contaminate each other with vapor. Now start the oven. Deionized water will not boil visible even if the regular water boils until the glass becomes dry. Be careful as overheated water can explode if it becomes contaminated!!
This experiment shows you practically about your skepticism if water is an absorbent at microwave oven frequencies. Water is not ideal but without doubt an absorbent. It also gives some important information about vapor, maybe needed in future experiments, explained a bit down.
Now the gold.
Place also a few of your gold particles in between these glasses.
Five minutes in the oven and the only heating that will occur is not due to 2 GHz waves from the oven, it is due to IR radiation from boiling water and that will be a very moderate heating.
You can easy try this in any microwave oven if you want to convince your self.
With this knowledge, what do you think happens if you place gold particles directly in water in a microwave oven? Correct, particles will be heated by water.
Similar thing as when a I leave the spoon in my coffee mug, when heating coffee in the microwave oven. The spoon will be warm, and even warmer a short period afterwards.
Do not know why it is important to first heat the gold part or why water must be used as solution or what size these particles have or dispersion thickness which can make my assumptions wrong, but with rather basic thinking, I had used a frequency where gold with this size works as a good absorbent, and water as a less good absorbent. A too obvious idea maybe? Lets check anyway...
Assume a nano-particle length of 100 nm. A dipole antenna with 100 nm length is in the range of UV light. A gold particle with this size will therefore be a good UV absorbent. Water can by good reasons be assumed to be a less good absorbent at this frequency, as it is very transparent at visible frequencies and if you have been diving in a clear sea you had probably noticed that blue tint seems less attenuated then IR/Red therefore seems UV to be a good frequency that is meeting your requirements. But no sunshine without sunspots. Direct heating of gold in water will cause water vapor rater quick as now is it the gold that is heating water. Vapor is rater different compared to water and acts as UV isolator, causing radiation chaos and blocks direct heating of the particle and instead is more water heated. Even at room-temperature will a thin vapor layer cover the gold surface. There is however a thermic transportation delay until too much vapor is produced which gives you a short period when it is possible to heat the gold particle more then surrounding water.
If you want to reach temperatures above 100 C or even 1000 C and have some control about what you is doing, must needed amount of power over time now be calculated. Useable pulse length can be in range of maybe max 0.1 nS depending on how high temperature you want to reach and how pure your water and gold particles are, so this solution is maybe not possible if it requires too much power during a too short period. It is relative simple to calculate power requirements if you know weight and size of your particles for a given particle-area were heating should occur during a short time frame. Knowing this can we now sort out if radiation pattern and intensity of the beam is in a reasonable power-range for for example common available UV-lasers. Time-frame can be increased by avoiding vapor.
According to this proposal, generated heat have not reached the particle by IR-radiation, instead is UV-radiation used for transferring of energy which makes is possible to heat the particle more then surrounding water.
If a short enough time frame is used for the UV pulse, is amount of direct heated water very low compared to heat generated in the gold particle.
DC current and two etched probes at 100 nm distance in your water solution will also work without directly heating water, but with less good taste as my previous experiment showed.