Fill 3.5-inch peat pots with sterile potting soil containing a small amount of perlite. Pack the soil firmly into the pot to eliminate air pockets.
Arrange the peat pots on a lattice-bottom nursery tray to make them easier to handle. Avoid solid-bottomed nursery trays since they hold too much moisture and do not conduct heat as effectively.
Sow two Cucurbita pepo seeds in each peat pot. Press the seeds 1/2 to 1 inch deep depending on the variety of Cucurbita pepo being germinated. Bury zucchini seeds at 1/2 inch and pumpkin seeds 1 inch deep.
Mist the soil in each peat pot five or six times using a spray bottle. Stick your fingertip into the soil to test if it is moist at a depth of 1 inch. Maintain moisture at that depth during germination.
Place the lattice-bottom nursery tray on a warming mat near a source of bright light such as under a strong fluorescent lamp or beside a large window. Set the temperature on the warming mat to 85 degrees F during the day and 68 F at night.
Watch for germination in one to two weeks depending on the strain of Cucurbita pepo. Remove the weaker or less vigorous of the two seedlings from each peat pot.
Keep the Cucurbita pepo seedlings indoors on the warming mat until after the last frost then plant them out in a sunny bed once soil temperatures reach 70 F.