Thermarest's Instant Field Repair Kit makes a repair using an instant adhesive, so the mat can be used as soon as its repaired.
Thermarest says:
The Instant Field Repair Kit makes fast, easy and lasting mattress repairs in the field. It includes all the same great self-adhesive patches that now come included with most Therm-a-Rest mattresses, and is just the insurance you need to prevent unexpected damage to your mattress from ruining your trip. Works on all current Therm-a-Rest mattresses.
Kit includes: (3) Alcohol Prep Pads, (6) Glue Dots and (3) Cover Patches and Instructions
Thermarest's Instant Field Repair Kit uses sticky adhesive 'dots' to glue down a patch instantly to cover a hole or small tear in a mattress. The glue dots don't need to 'cure' like some adhesives and so the mat can be used straight away after a repair.
For a stronger more permanent repair you can use the Thermarest Permanent Home Repair Kit - the main difference is that the glue used in the Permanent kit needs 4 undisturbed hours to 'cure' before the repair is complete - which could be impractical on a trip.