I concur with the above. Mod Podge will soften with heat. I'd likely either use spray adhesive or PMA. You can dry mount it, but be aware that you 100% need a true release sheet, not just plain paper or something. When the acrylic softens, it gets tacky becoming almost an adhesive itself.
My pet method of dealing with jigsaws was to mount them onto MDF with the same spray glue I used for mounting prints and posters. It was applied with a spraygun, not the almost useless rattle can spray glue.
The step by step process was:
Sandwich the jigsaw between two sheets of card or MDF, turn it over and remove the top sheet so that it sits image side down on the lower piece.
Prepare several strips of matcard of the same thickness as the artwork and have these handy.
Cut a backing board oversize by a couple of inches, mark where the jigsaw is to sit then spray is with glue.
Place the glued board over the jigsaw, line it up as best you can on the marks and press it down firmly by hand or use a roller.
Turn the mounted piece over and use the strips to cover the remaining glued area.
Give it a good squeeze in the vacuum press or use a roller to get a final tack.
Trim the board to the correct size.
You could do something similar with a sticky board but the spray glue I used was a lot less "grabby" and some repositioning was possible.