Solidoodle 3 bed won't heat above 68 degrees

1. unplug it from the board 
2. remove the bed leveling screws and remove build plate
3. gently peal old heat pad from build plate
4. apply new heat pad in its place
5. route the wires and plug into the board
6. hope it works better than the old one
7. plan to switch to SSR and AC/500W heat pad because your tired of waiting for the bed to heat up

The new pad didn't come with adhesive backing?

It shouldn't tear when you pull it off just be carefu.l As far as glue goes I really don't know what you can use.
I just looked at my old heat pad and the adhesive pulled off and I don't remember if the bed was still sticky or not.
I would look at some spray adhesive if it doesn't stick it will just fall off and you'll have to try something different.
Wish I could be more help.

Have you hooked this new bed up to make sure it works when connected to the printer?

Also you might check your old one compared to the new one to see if the warping is better or worse.

there are plenty of high temp glues available just make sure you get one that stays flexible when cured, I think even gorilla glue can handle 100C but I have seen quite a few rated past 500F

You bet....
Did you get it working?

It's a good idea to have it in place.  If you don't have any other way to stick it to the bed you can use another piece of thin sheet metal to sandwich it in place that is how I have mine set up.  Can get what you need at most local hardware stores. Just cut to size and drill three holes (make sure the holes are not bigger than the springs).

I went this route because my insulation kept falling off.

You can use a spray adhesive. As far as the motor goes I have been running mine that way since June.  I think the Z-motor has a lot of extra power.  The small amount of weight from a thin piece of sheet metal is less than the glass most are using.
Not to mention the guys using ceramic tile for the bed.