There is a matrix of performance for most cleaning applications, this generally applies to grease/oil/fat type of soil.
Cold water is not as good as cold water + chemicals,
is not as good as hot water,
is not as good as hot water + chemicals.
Hot water over 140F (60C) will soften and release grease/fat/oil.
Using the formula for impact force: (Flow x Square root of Pressure)/18.92 shows the following:
1 GPM @ 4000 PSI = 3.34#
2 GPM @ 2000 PSI = 4.73#
4 GPM @ 1000 PSI = 6.69#
All the above have the same 'rating' of "Cleaning Units". However the 2 GPM unit will clean ~29% faster than the 1 GPM unit and the 4 GPM unit will clean ~50% faster. If you keep the pressure the same at 2000 PSI then the numbers work out as follows:
1 GPM @ 2000 PSI = 2.36#
2 GPM @ 2000 PSI = 4.73#
4 GPM @ 2000 PSI = 9.45# or the 2 GPM unit will be ~50% faster and the 4 GPM unit will be ~75% faster.
Pressure is the easy part of the performance equation, this is why you only need the square root of that value.
Flow is directly related to Horsepower, more of one requires more of the other.
A vast percentage of cleaning can be done quite efficiently, with minimal chance of damage, at 4 GPM @ 2000 PSI. Most contract cleaners are limited by water supply to 5.5 GPM because this is the average available flow from municipal and rural sources. Carrying a 100+ gallon tank will offset some of the impact of low flow versus demand.
As to your original question you can expect to pay from $1000 to $2500 for a hot box/heater module. the difference is in the details; thermostat, burner control switch, fuel (diesel or propane), burner (12V, 110V or milivolt), portable or stationary, painted or stainless steel, safety certified or not and so on.
The requirement of having hot water is limited to what you are cleaning; if you do not encounter grease/fat/oil in your jobs then cold water will work perfectly fine. Know what you are cleaning and adjust your method to the surface.
Experience, information available from BBS's and local professional pressure washer dealers and contract cleaners can and should be your best source of information on how to proceed.
Sorry for the long winded response, hope this helps? Cheers.