Deborah Fenlon's Menos 4 trial will investigate how routine CBT could help patients regain a sense of control over difficult side effects.
Hot flushes and night sweats are experienced by about 70% of women undergoing treatment.
The trial has been funded by a Â£300,000 Breast Cancer Now grant.
Royal Glamorgan Hospital is one of six participating in the three-year project, led by Swansea University's Prof Fenlon.
Hormone replacement therapy, normally offered to women experiencing hot flushes as part of the menopause, cannot be used by women with breast cancer as it can increase the risk of their disease returning.
The scientists said although CBT was known to be effective, it was not routinely offered on the NHS for women with breast cancer and can only be given to groups by trained clinical psychologists.
During the study, half the women will receive group CBT from a specially-trained breast cancer nurse in six weekly sessions lasting 90 minutes. The other half will receive whatever support they would normally receive.
A 52-year-old teacher, taking part in the trial, said: "I had never expected hot flushes to be quite so awful.
"Some nights I just do not sleep as the hot sweats keep me awake and then I have to work the next day as though everything's ok and it's not."
Prof Fenlon said: "Hot flushes and night sweats can have a major impact on women's lives; affecting their work, social life and disrupting their sleep.
"There are very few effective measures to help support women with this problem, particularly after breast cancer and proven interventions are not widely available.
"With this study we hope to show how an effective intervention can be offered more widely."

Light-flyweight Yafai, 23, scored a clear points victory over Cameroon's Simplice Fotsala in the round of 32.
Welsh lightweight Cordina used classy footwork and counterpunching to beat bustling Filipino Charly Suarez.
Okolie, a heavyweight in just his 26th bout, used his jab well to overcome Polish fighter Igor Jakubowski.
The 23-year-old Londoner only quit his job at McDonalds after watching Anthony Joshua win super-heavyweight gold at London 2012, and battled obesity as a youth.
"To become a legend, you have to do legendary stuff. This is just part of the journey to be a legend," he said.
"If I manage to win, then I deserve it. It's not about scraping a medal or getting lucky. It's about wanting to beat everyone. If I can beat everyone in front of me, I get gold. If I don't, I don't deserve it."
Light-heavyweight Joshua Buatsi is the only Briton in action on Sunday, taking on Uganda's Kennedy Katende at 17:00 BST.

He was convicted of contesting crimes against humanity.
The former Front National chief was convicted of the same charge in 2012 after saying France's Nazi occupation had been "not particularly inhumane".
France has strict laws against Holocaust denial.
Mr Le Pen told a journalist his remarks "corresponded to my thought that the gas chambers were a detail of the history of war".
Asked if "millions of deaths" could be called "point of detail", Mr Le Pen said: "It is not a million deaths, it is the gas chambers. I'm talking about specific things. I have not talked about the number of dead. I spoke of a system. I said it was a detail of the history of warfare."
As well as remarks about the Holocaust, Mr Le Pen said in 2014 that the Ebola virus could solve Europe's "immigration problem".
He was expelled from the party he founded last year by his daughter Marine Le Pen, the current leader, over his extreme beliefs.
In 2015, Ms Le Pen was acquitted of inciting hatred after comparing French Muslims to the Nazis who occupied France during the war.

It followed a "network-wide failure" that caused delays, a Metrolink spokeswoman said.
There had been a communications failure between the control room in the depot and trams on the network, she added.
Metrolink boss Danny Vaughan said: "I'd like to apologise once again and thank passengers for their understanding."
There is no indication the fault was caused by hacking.
In May, the tram network was shut down because control room staff lost visible sight of trams.
A Swansea scientist is trialling how cognitive behavioural therapy could reduce the impact of hot flushes for breast cancer patients.
[NEXT_CONCEPT]
British fighters Galal Yafai, Joe Cordina and Lawrence Okolie progressed in the Olympic boxing competition on the first day of Rio 2016.
[NEXT_CONCEPT]
Former French far-right leader Jean-Marie Le Pen has been fined 30,000 euros (Â£24,000; $34,000) for calling the Nazi gas chambers a "detail" of World War Two.
[NEXT_CONCEPT]
All tram services have resumed in Greater Manchester after the whole network shut down on Saturday following a communications problem.