While at the local feed store a few weeks ago, the clerk commented that Lamb was considered a "hot" meat and that I shouldn't feed it during our hot Arizona summers. She said that some meats require more metabolic process to break down and actually make the dogs feel hotter during digestion. Any truth to this? If so, what other meats would fall under this category?

I suspect she was referring to Ayurveda.
Ayurvedic medicine: A whole medical system that originated in India. It aims to integrate the body, mind, and spirit to prevent and treat disease. Therapies used include herbs, massage, and yoga. (also called AyurvedaA whole medical system that originated in India. It aims to integrate the body, mind, and spirit to prevent and treat disease. Therapies used include herbs, massage, and yoga.) is one of the world's oldest medical systems. It originated in India and has evolved there over thousands of years. In the United States, Ayurveda is considered complementary and alternative medicine (CAM). A group of diverse medical and health care systems, practices, and products that are not presently considered to be part of conventional medicine. Complementary medicine is used together with conventional medicine, and alternative medicine is used in place of conventional medicine.--more specifically, a CAM whole medical system. A complete system of theory and practice that has evolved over time in different cultures and apart from conventional medicine. Examples of whole medical systems include traditional Chinese medicine, Ayurvedic medicine, homeopathy, and naturopathy. Many therapies used in Ayurveda are also used on their own as CAM--for example, herbs, massage, pressing, rubbing, and moving muscles and other soft tissues of the body, primarily by using the hands and fingers. The aim is to increase the flow of blood and oxygen to the massaged area., and yoga.
http://nccam.nih.gov/health/ayurveda/

In ayurveda, foods are also categorized as heavy or light, dry or unctuous/liquid and warm or cool (temperature), and different qualities balance different doshas. A balanced main meal should contain some foods of each physical type. Within this overall principle, you can vary the proportions of each type based on your constitution and needs for balance, the season of the year and the place you live.
http://www.pioneerthinking.com/ss_ayurvedicdiet.html

According to Traditional Chinese Medicine (TCM) meats do have qualities (for more information get the book Four Paws Five Directions). I'm trying to understand it all. I do know that chicken and lamb are considered warm meats and I avoid feeding them to Brandy as she has an internal heat and dampness problem. I feed fish, beef, pork.

Black Labbies (Lisa) knows much more about this and can probably explain it better than I.

TCM:http://www.ontcm.com/healthy/foods.htm

The four natures
Foods, the same as herbs, could also be classified into "four natures" i.e. "cold", "hot", "warm" and "cool" in line with their actions and curative effects. The foods of "cold" or "cool" property can be used to treat hot-natured diseases; while the "hot" or "warm" foods are used in treating the cold-natured diseases. Some foods may be neutral in nature.The following are listed the foods in different natures:

1). Food are cold or cool in natue: Barley, millet, buckwheat, greenbean, coix seed, celery, spinach, lettuce, green cabbage stems, turnips (white), bamboo shoot, lily bulb, lotus root, eggplant, tomato, water melon, white gourd, sponge gourd, cucumber, bitter melon, apple, pear, orange, banana, rabbit's meat, frog's meat, duck's meat, duck's egg, crab, sea couch(es), fresh water snail, kelp, laver, green tea, soy sauce, table salt, rock candy.

2). Foods are hot or warm in nature: Glutinous rice, Chinese sorghum, pumpkin, hot pepper, ginger, scallion, onion, leek, funnel green, garlic, parsley, mustard greens, date(s), walnut kernel, plum, arbutus, pomegranate, longan, peach, cherry, apricot, chestnut, pineapple, spirit, vinegar, black tea, pepper, coffee, chicken, turkey, sparrow's meat, mutton, vineson, dog's meat, spotted silver carp, grass fish, trout, red sugar.

3). Foods are neutral in nature: Polished rice, wheat, corn, soybean, pea, small red bean, cabbage cauliflower, carrot, fungus, silver fungus, mushroom, yam, day-lily buds, peanut, potato, lemon, grapes, cherry apple, olive, lotus seed, pork, beef, goose meat, spring chicken, pigeon's meat, quail's meat, egg(s), quail's egg, carp, mandarin fish, eel, yellow croaker, turtle, jelly fish, abalone, white sugar, honey, jasmine tea, wulong tea.