So I thought to perhaps have 3 of the same voltage regulators in Parallel to power the Relay board to hopefully share the load /heat.
No that would not work.
You are dropping 12 - 5 = 7 volts across the device so any current is going to turn into a bit of power that the regulator burns off. Yes it will get hot, this is normal and to be expected.
If it gets too hot to touch then consider a bigger heat sink, maybe even get some silicon heat sink compound to make the metal / case junction more thermally efficient. At the worst there is a thermal trip in those regulators that will shut down if it gets too hot.
Actually zinc-oxide heat sink compound is the stuff. silicone itself is not a
good heat conductor. The zinc oxide particles may be in a silicone oil
base or some other grease. There are other materials available, some
as thin rubber-like sheets that also act as insulators (not normally
needed for voltage regulators where the tab is usually ground).
I reckon the copper-filled grease used for preventing car brakes squealing
has to be the best heat-sink compound (surely?) Perhaps there's a risk it drips
onto the rest of the circuitry though.
Thermal conductor types
Thermal greases use one or more different thermally conductive substances:
Ceramic-based thermal grease has generally good thermal conductivity and is usually composed of a ceramic powder suspended in a liquid or gelatinous silicone compound, which may be described as 'silicone paste' or 'silicone thermal compound'. Thermal grease is usually white in colour since these ceramics are all white in powder form. The most commonly used ceramics and their thermal conductivities in units of W/(m·K) are:[4]
beryllium oxide 218
aluminum nitride 170
aluminum oxide 39
zinc oxide 21
silicon dioxide 1
What is that last one again?
Silicone is in fact a good insulator, I have several kitchen mats made of the stuff and a few baking trays.
6V might be too low - check the data sheet for your regulator.
Can be seen with notes and conditions in table such as:
Vout, with Vin - Vout >= 1V (or more).
Hi, what are you using as your 12Vdc, can you send us a pic, also can you measure the 12Vdc input the reg board and the 5Vdc output on the reg board when this condition occurs?