What temp is the 'closet' during the daytime with the lights all on? It may be less expensive to heat the whole space to the desired temp with a space heater. You'll want a good soil temp. probe thermometer if you don't have one.
Remember that to hot will stiffle germination just like to cool, so a heat mat controller is a must IMHO.
Also, remember that while germination takes place at optimum temperatures, once germination happens, the optimum temperature changes to what is called the 'grow on' temperature. This temperature is often cooler to help limit the stretching of your plants under the lights.
Ultimately, this means I am cycling plants onto heat for germination, then back off the heat for continued growing.
Here's an example of how this can be explained for sprouting and then growing tomato seedlings:
Johnnies seeds said:
For tomato:
Keep (germination mix) at 75–85°F (24–29°C) with moderate moisture. At first true leaf, pot-up to 50-cell trays or 4" pots, depending on expected transplant timing. Grow at constant 60–70°F (16–21°C) temp
So tomatoes = 75-85 for germination, then temp should drop to 60 - 70 for optimal continued growth.
Only in the germination stage then is my heat mat used for tomatoes. So, with planning- I start my seeds in succession, slowest growers first- on the mat.
I know this wasn't the answer you were seeking... but maybe you don't need the heat mat space under every tray?
