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If the high heat does not persist, the plant will produce side shoots. But if the heat continues and you see the whole plant start to yellow, then the plant is lost and you should start over when the temperatures start to cool off again.

It sounds like Fusarium Wilt. You can read more about it here:
https://www.gardeningknowhow.com/plant-problems/disease/controlling-fusarium-wilt.htm
If your pea plant was in a container, dispose of the soil and bleach the pot before using it again. If it was in the ground, you can sterilize the soil by covering it with black plastic and cooking the Fusarium fungus to death.

Carrots and most root vegetables do not transplant well. If they survive you usually don't end up with a usable crop. The peas can be transplanted if they are still small, and you move them with the majority of their root ball intact. You need to plant at the same depth as their prior location and similar soil is helpful. If they were in the shade than I would suggest moving them on an overcast day. Because peas germinate quickly you may just consider sowing a new lot. I would suggest sowing new carrots as well. Enjoy your garden.

If the weather is warm, this can cause issues with this cool weather crop.

I suspect that your soil may be too high in nitrogen. You can try an application of Bone Meal to increase Phosphorous.

https://www.gardeningknowhow.com/edible/vegetables/peas/how-grow-peas.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

This could be a small number of things. Most commonly, this is due to there being too much nitrogen in the soil. This can be offset by adding phosphorus and potassium, along with dolomitic lime to the soil. This article will help you in the meantime: https://www.google.com/url?q=https://www.gardeningknowhow.com/edible/vegetables/peas/growing-snap-peas.htm&sa=U&ved=0ahUKEwjN5OTixY_ZAhUKDiwKHW_oD1YQFggYMAc&client=internal-uds-cse&cx=009296322515861343460:jftykenwinc&usg=AOvVaw1hFZ9RQdrKZMz4YgL3zPmM

It doesn't sound like there is much in the way of potassium and phosphorus, and LOADS of nitrogen.

Peas harvest their own atmospheric nitrogen. Adding more (manures) will lead to poor flowering. Lacking in phosphorus and potassium will prevent the formation of flowers or fruit. The article is for sweet peas, which are the toxic sister of the edible pea, but they are treated the same: https://www.gardeningknowhow.com/ornamental/flowers/sweet-pea/sweet-peas-not-blooming.htm